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2014
Winning Recounts: Essential Mathematical and
Statistical Insights for Election Lawyers
Brian C. Kalt
Michigan State University College of Law, [email protected]
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Brian C. Kalt, Winning Recounts: Essential Mathematical and Statistical Insights for Election Lawyers, 30 J.L. & Pol. 141 (2014).
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Winning Recounts: Essential Mathematical and Statistical
Insights for Election Lawyers
Brian C. Katt•
Many lawyers joke that they went to law school because there is no
math required. Unfortunately for them, mathematics is ubiquitous in the
law, and the lawyers who cannot do it well are at the mercy of those who
can. Election recounts are a prime example. Recounts happen, candidates
rely on lawyers to win them, 1 and to do so those lawyers need to grasp the
mathematics of recounts.
This Article uses basic mathematics and statistics to construct an
optimal general strategy for election recounts. As it happens, this strategy
tracks the conventional wisdom espoused by leading election lawyers.
More important than providing new mathematical support for this
conventional wisdom, though, is providing a mathematical explanation for
the persistent resistance to it.
This resistance seems to be rooted in the admonition that recount
challengers fight to recount most subgroups of votes that are expected to
favor their opponents? This advice is counterintuitive to recount
neophytes, but it is nevertheless correct. A principal objective of this
Article is to explain and defend this counterintuitive requirement so that
more candidates and lawyers embrace it.
In doing so, they can avoid the fate that befell the most famous recount
challenger in recent American history: AI Gore in the 2000 presidential
election. Notwithstanding his slogan of "Count Every Vote," 3 Gore and his
team sought only partial recounts. 4 This strategy violated the mathematical
• Professor of Law and Harold Norris Faculty Scholar, Michigan State University College of Law.
An earlier version of this Article was presented to the annual meeting of the Public Choice Society &
Economic Science Association. Thank you to the other participants and commenters; to Bernard
Grofman for inviting me to deliver that paper; to Dennis Gilliland, Raoul LePage, and Jasjeet Sekhon
for their assistance on statistical matters; to Barbara Bean, Scott Nagele, Courtney Soughers, and Ann
Vaught for their research assistance; and to Daniel Bamhizer, Hon. Danny J. Boggs, Michael
Sant' Ambrogio, and Jorge E. Souss for their helpful comments.
1
See TiMOTHY DOWNS ET AL., THE RECOUNT PRIMER 2 (1994).
2
See irifra Part I. B.
3
If every vote had been counted, Gore could have defeated George W. Bush. See Dennis Cauchon
& Jim Drinkard, Florida Voter Errors Cost Gore the Election, USA TODAY, May II, 2001, at AI
(showing that a statewide recount that included undervotes and overvotes offered Gore a significant
possibility of victory).
4
Gore's team actually argued in court against a more complete recount. See, e.g., JAKE TAPPER,
141
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Journal ofLaw & Politics
[Vol.XXX:141
and statistical precepts that this Article will illuminate, and even ran
contrary to the advice of his own recount lawyers. 5 While this math and
advice may have been counterintuitive, Gore's resistance to them probably
cost him the election. 6
Part I of this Article derives some elementary mathematical principles
of optimal recount strategy and compares them to the conventional wisdom
of recount experts. Part II applies this optimal strategy to the 2000
presidential recount, looking only at what the parties knew or should have
known at the time. It concludes that Al Gore's strategy was mathematically
unsound in ways that required no hindsight to realize. Part III summarizes
the discussion and offers concluding advice for would-be recount
challengers and their lawyers.
I. OPTIMAL RECOUNT STRATEGY
Recount strategy starts with two very simple facts: (1) if an election is
very close and you lost, you might want to seek a recount; and (2) if you
are ahead, you will want to avoid one. Admittedly, these are not
groundbreaking insights.
More useful, but more complicated, is the math that emerges once other
factors are introduced. The most important mathematical concept is
uncertainty, which can also be expressed as variance (i.e., how widely
spread out the range of possible outcomes is). This Part will examine
variance and how it interacts with other factors in a recount. From that
analysis, it will derive several principles of mathematically optimal recount
strategy. After formulating these principles, this Part concludes by
reconciling them with the conventional recount wisdom espoused in The
DOWN AND DIRTY: THE PLOT TO STEAL THE PRESIDENCY 412, 414 (2001) (recounting David Boies's
argument to Florida Supreme Court on behalf of Gore).
5
See WASHINGTON POST, DEADLOCK: THE INSIDE STORY OF AMERICA's CLOSEST ELECTION 7778 (2001) (describing internal battle in Gore camp); TAPPER, supra note 4, at 66-68, 193-94; JEFFREY
TOOBIN, TOO CLOSE TO CALL 37-39 (200 I).
6
Gore's requested recounts would not have reversed the election result. See Amy Driscoll, Dade
Undervotes Support Bush Win, MIAMI HERALD, Feb. 26, 2001, at lA (reporting media analysis of
undervotes in Miami-Dade County, the only Gore-requested recount not performed). For that matter,
the statewide partial recount ordered by the Florida Supreme Court--over Gore's objection-almost
certainly would not have reversed the result, even if the United States Supreme Court had not
intervened to stop it. See Dennis Cauchon, Newspapers' Recount Shows Bush Prevailed, USA TODAY,
Apr. 4, 2001 (reporting media analysis of undervotes). See generally Steve Bickerstaff, Post-Election
Legal Strategy in Florida: The Anatomy of Defeat and Victory, 34 LoY. U. CHI. L.J. 149 (2002)
(detailing Gore's strategic failures). Only a full count offered Gore any hope. See supra note 3.
2014]
Winning Recounts
143
Recount Primer, a definitive practical guide written by three top recount
experts a few years before they worked in vain to help Al Gore.
A. Underlying Assumptions
Before digging into the mathematical muck, a few assumptions need to
be set forth. First, this Article assumes that both the putative winner of an
election (the "defender") and the putative loser (the "challenger") are
rational actors who seek to maximize their net benefits. This means that
challengers should seek a recount only when their benefit in doing so
exceeds their costs. The assumption that people act rationally is widely
used in economics and is highly contested-and justifiably so-but that
does not undermine the notion that candidates should be rational here.
While figuring out what counts as "costs" and "benefits" can get slippery,
candidates surely should do what is best to achieve their goals, whatever
those goals may be.
Second, this Article assumes that the challenger is an "underdog" with
less than a 50% chance of prevailing. Considering that recount challengers
rarely win/ this assumption is reasonable enough. Challengers do
sometimes get a better-than-50% chance of prevailing, and when that
happens they may need to switch over to the strategies of a rational
defender (and vice versa). When that happens in this Article, it will be
noted and treated accordingly.
The third and most crucial assumption is that the decision to pursue a
recount entails multiple sub-decisions. In 2000, Florida had sixty-seven
counties, for instance, each with its own independent election officials. But
even in elections involving only one jurisdiction,8 there may be different
levels of potential recounting to seek: singling out particular precincts;
inspecting the counting machines; repeating the machine count; hand
counting some ballots; hand counting all ballots; and so on. Where
recounts are an ali-or-nothing proposition, there is not much strategy to
consider beyond the non-groundbreaking insight that opened Part I: seek a
recount if you lost narrowly. Where there is the potential to subdivide,
7
See Bickerstaff, supra note 6, at 159 (noting that recounts generally only change a handful of
votes); Jim Drinkard, Fla. Results Unlikely to Change, USA TODAY, Nov. 9, 2000, at 12A (making
point more generally).
8
Florida law passed in the wake of the 2000 recount now makes it much more likely that statewide
races will have only statewide recounts. See FLA. STAT.§ 102.166(1) (2011).
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[Vol.XXX:141
though, challengers must consider separately whether to seek a recount for
each individual component. That is where the math comes in.
Fourth and finally, most of the factors considered in this Article cannot
be quantified precisely. Some defy quantification because they are based
on necessarily incomplete data-after all, the whole point of a recount is to
search for information that is as yet unknown at some level. Other factors,
like "political costs," defy precise quantification because they are not very
tangible. Because perfect precision is impossible, a challenger cannot
really use the principles derived in this Article to determine that, say, he or
she would win a recount if it excludes all of County A except for Precinct
B. This Article instead offers a framework for generally understanding how
to maximize the chances of winning a recount.
B. Challenger Strategy
All other things being equal, a challenger's chances of winning a
recount are maximized when uncertainty is maximized, which first and
foremost means maximizing the number of votes being re-examined. In
real recounts, however, all other things are not equal; sometimes
challengers can expect a particular subset of votes to favor them or favor
their opponents. But the effect of uncertainty is so significant that
challengers should pursue groups of votes that they expect will favor their
opponents, unless they are sufficiently certain about that result.
Reaching these conclusions requires laying some groundwork. It also
requires exploring certain nuances that the rest of this section will address.
I. Basic Variables and Terminology
As already mentioned, a challenger should seek a recount only if the
benefit of doing so exceeds the cost. The challenger's most obvious benefit
from seeking a recount is the possibility of reversing the election result.
That can be expressed mathematically as the value of winning the recount
2014]
Winning Recounts
145
multiplied by the probability that the challenger will do so. 9 Some other
costs and benefits of recounts are discussed later. 10
The probability that a recount will be successful (P) is a function of
three variables. First, what is the defender's initial margin of victory (M)?
Second, how many net virtual votes ( Vnet) will the recount produce for the
challenger? Third, what is the chance that those virtual votes will be
legally translated into actual votes (L)?
A "virtual vote" (V) is one that is not reflected in the initial tally, but
that potentially could be added in a recount. There are many forms that a
virtual vote can take. A machine could fail to count a ballot in the initial
count, but a reinspection would count it. The initial count could doublecount a ballot, and reinspection could correct this error. The initial count
could reflect a simple tallying or recording error, which reinspection would
undo. Ideally the recount will be more accurate than the initial countrecounts tend to be slower, more deliberate, and more carefully
scrutinized-but this is not necessarily so. Indeed, a virtual vote could also
come from the second count introducing an error.
Some virtual votes may favor the challenger ( Vchaflenger) and some the
defender (Vdefender). To have a chance to reverse the election result, the
challenger needs to find a net advantage among virtual votes (Vchaflenger Vdefenden or Vnet) that is greater than M II
Just finding enough net virtual votes will not suffice for a challenger,
though. Before it can actually be added to the tally, a virtual vote must be
legitimized though some judicial or administrative action. Such legal
actions do not occur automatically; the challenger's probability of finding
enough net virtual votes must be discounted according to the probability
that he or she will prevail in this legal process ("legal translation" or L).
The Florida recount provides a striking example of this. While statisticians
have established that the "butterfly ballot" in Palm Beach County almost
9
Already we can derive a general principle of recount strategy. Because victory will almost
certainly be a benefit (assuming that the challenger still wants to hold the office for which he or she
was running) pursuing a recount will represent some benefit for the challenger however remote the
probability of victory. After all, the alternative-no recount-has zero chance of delivering him or her
the prize. If the challenger is to reject the idea of a recount, then, it will be because of some other part
of the cost/benefit balance, not just because winning is a long shot. This helps explain why so many
recounts are sought even though so few are successful.
10
See infra Part 1.8.9.
11
Challengers can also win when V"" equals M exactly, if they then win the tiebreaker. This pesky
consideration will not prove significant in this Article.
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Journal ofLaw & Politics
[Vol.XXX: 141
certainly caused thousands of Gore voters to accidentally vote instead for
Pat Buchanan, Gore knew that there was no way under the law to use that
evidence to change the tally in his favor (L was very close to zero), and so
he wisely did not try. 12
2. Expected Value and Variance
Although P is a function of M, Vner, and L, it can be understood more
generally as relating to expected value and variance. In layperson's terms,
a challenger's chance of winning a recount is a function of how he or she
expects the recount to tum out, and how sure he or she is about that.
Assuming (as this Article does) that the challenger is an underdog-that
he or she will most likely lose the recount-then the expected value of a
recount effort is less than M In the graph below, the portion of the area
under the curve that is to the right of the vertical line at M (the "victory
section") represents the challenger's probability of winning the recount:
0
M
Net votes picked up by challenger
The effect of increasing expected value-moving the curve to the
right-is obvious. The more votes the challenger can expect to net on
average, the better his or her chances of winning the recount will be.
Compare the first graph below (in which the expected value of the recount
is zero 13 ) with the second (in which the expected value is greater than
zero):
12
See TOOBIN, supra note 5, at 55, 200 (describing the Gore team's assessment of prospects
regarding the butterfly ballot); Bickerstaff, supra note 6, at 172-77 (describing butterfly ballot
problems and the Gore team's response to it).
13
The expected value is the average of all the possible results, weighted by probability. In the
diagrams in this section the possibilities are symmetrical, so the expected value is not only the average,
but also the median (middle) and mode (most likely).
2014]
Winning Recounts
147
In the second graph, the victory section is still less than 50% (the
expected value, while positive now, is still less than M), but it is much
greater than in the first graph.
Increasing variance-making extreme results more likely, and so
making the graph wider and flatter-helps the challenger as well. Compare
the two graphs below, in which the total areas under the curves are the
same and the expected values are the same, but the variances are different.
In the first graph the variance and its square root, standard deviation, are
lower than in the second graph:
0
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Journal ofLaw & Politics
[Vol.:XXX: 141
The victory section is larger in the second graph: increasing variance
helps the challenger's odds even without any change to expected value.
An important note: These graphs exhibit the classic bell curve that one
gets from a "normal" distribution. A two-party race can be modeled with a
binomial distribution, the same as would be used to graph how many coin
flips out of a group came up heads. If the numbers are large enough, a
14
binomial distribution will approximate a normal distribution.
As
discussed later, though, binomial and normal distributions are not really the
correct ones to use when thinking about recounts, a fact that makes a
tremendous difference. 15 For now, bell curves will do to make the point
that variance matters.
The discussion that follows turns to other variables, but the impact of
these other variables will always come from their effect on expected value
or variance.
3. Number of Votes
Perhaps the simplest variables affecting P are the number of votes being
re-examined (n) and the number of votes being changed (V).
These are two very different numbers. A recount could examine 100
ballots, but have only 5 votes that change upon re-examination: n equals
100, V equals 5. Alternatively (though less commonly), the recount could
focus on a precinct with 5 votes in it but "change" 100 of them when a
cache of previously undiscovered ballots is found there: n equals 5, V
equals 100. 16 This relationship can be expressed in terms of "yield," or the
ratio between the number of virtual votes and the number of votes in
question (VI n), but yield does not add much to the analysis as a variable
separate from n and V. 17
V is more directly significant than n, but it is also much harder to
predict. Participants in a recount will always have a fairly accurate idea of
how many ballots are being re-examined, but unless some recounting has
already been done they can barely guess how many votes will actually
14
See DAVID S. MOORE, THE BASIC PRACTICE OF STATISTICS 348 (2010) (discussing use of
normal distribution to approximate binomial distribution).
15
See infra Part 1.8.5.
16
V can also be negative, such as when a recount discovers double counting in the original tally.
17
Yield mainly just determines V from a known value of n. If we hold V constant (i.e., if we
compare the two situations, nhigh · Y,o .. and n,o... · Yhigh, where the products are equal), the expected value
of the challenger's net gain in a recount will not change. The variance may change a bit, but the effect
is quite small unless the virtual votes are skewed heavily to one candidate.
2014]
Winning Recounts
149
change. Still, generally, the more votes that are re-examined, the more
votes will probably change. The higher n is, the higher V will probably be.
An increase in n or V will increase variance and so, all other things
being equal, a higher n or V means a higher P for the underdog challenger.
In other words, the more votes that are re-examined or changed, the better
the challenger's chances of winning the recount become. P will top out
somewhere below 50% if we assume, as we are at this point, that any new
votes are as likely to favor the challenger as the defender. When this
assumption of balance is in place, the expected value of the recount will
always be zero. Again, the gains here for the challenger from a higher n
and V will come solely from the effect on variance, and the challenger will
remain as the underdog.
4. Disparateness
Contrary to the assumption just discussed, we may not be able to
assume that a virtual vote is equally likely to go to either side. To be sure,
in many cases we will. There may be no data ex ante about the distribution
of new votes, or the change in a recount may result from a clerical error
and thus be equally likely to benefit either side. Additionally, if the only
source of data is the original count-which in typicai recount situations
will divide very close to 50-50-there will be near-symmetry if we assume
that the new votes will divide between the candidates in the same
proportion that the old votes did.
Once more nuanced data are known about the votes being recounted,
however, the chance that a virtual vote will favor the challenger may not be
50-50. This requires consideration of disparateness (D): the probability
that a virtual vote will go to the challenger as opposed to the defender.
The expected value of a recount for the challenger is (2D- 1) · V. Using
simple numbers as an example, if D is 60% and there are a hundred virtual
votes, the challenger can expect to get sixty of them while the defender can
expect to get forty, which means a net gain for the challenger of twenty
votes: ((2 · 0.60) - 1) · 100. The formula also shows why the expected
value of the recount was always zero when D equaled 50%; if D is 50%,
then 2D- 1 is zero.
When the expected value was zero, P still increased as n and V
increased, but only because of their effect on variance. If D exceeds 50%,
it is even more advantageous to the challenger to maximize n or V, because
this will increase the expected value, too. If D is greater than 50%, (2D 1) is positive, and the expected value of the recount will increase as n and
V increase. If V gets high enough, the recount's expected value might even
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Journal of Law & Politics
[Vol.XXX:141
exceed M, and the challenger will no longer even be an underdog. Of
course, any time that the challenger attempts to cherry-pick subsets of
recountable votes with a high D, the defender can try to stop that, or can do
the same with low-D votes. 18
The opposite effect occurs with those low-D (below 50%) votes: the
challenger will have a negative expected value, and it will get lower as n
and V increase. By analogy, consider whether your chances of beating Phil
Mickelson at golf are better if you compete on just one hole or if you play
seventy-two. While your chances of winning one hole are not good, they
only get more dismal the longer you play.
An interesting effect occurs when D is below, but fairly close to, 50%.
In that case, not only will P decrease more slowly as n and V increase than
it would if D were even lower, but P will also initially rise. This is because
P is being pushed in two directions as n and V increase. Because D is
below 50%, P is pushed downward by the decrease in expected value. At
the same time, though, P is pushed upward by the increase in variance.
When D is close to 50%, the effect of increased variance initially
outweighs the effect of decreased expected value. 19
18
The 2000 congressional race in the Eighth District of Michigan provides a perfect illustration.
After a very close race, the putative loser, Dianne Byrum, asked for a recount in the counties where she
had obtained the strongest support. The victor, Mike Rogers, requested a recount in all of the areas that
Byrum had left out. He recognized that he would be taking a risk if he let Byrum carry out a one-sided
recount. Although Rogers was confident of maintaining his lead, he was also confident that the areas
that supported him in the first count would likely add votes to his column if there was a recount.
(Michigan voting technology in 2000 was reliable enough that Rogers did not have to worry about
increasing the variance of the recount all that much.) In the end, there was a full recount, with each
candidate paying for the recount in the areas that favored him or her; Rogers won, but Byrum got a full
recount and paid for only part of it. See Amy Franklin, State Canvassers CertifY Election Results;
Byrum Asks for Recount, THE ARGUS-PRESS (Owosso, Mich.), Nov. 28, 2000, at AI (describing
Byrum's and Rogers's initial recount requests); Recount Starts in 8th District, DET. FREE PRESS, Dec.
5, 2000, at BI (describing recount process); David Poulson, Recount Adds Up for Rogers, GRAND
RAPIDS PRESS, Dec. 16,2000, at AS, available at 2000 WLNR 7809736 (describing final result).
19
For an illustration of how the effect works with a binomial distribution, assume that you are
playing roulette. You bet one chip on Red every time for a I: I payoff (you either win a chip or lose a
chip). Assume further that your goal is to net at least five chips, but that you must decide in advance
how long you are going to play. Now consider the following graph:
2014]
Winning Recounts
151
This effect leads to a very important but counterintuitive conclusion: up
to a certain point, it is to the challenger's advantage to seek to recount
more votes, even when each new vote the recount finds is more likely to
favor the defender.
The question, of course, is where this "certain point" lies. That requires
more analysis. For now, it is enough to say that recount participants need
to consider variance and not just expected value.
5. The Crucial Effect of Clustering
The simple examples earlier in this Article were based on a binomial
distribution, which assumes a series of binary events-like coin tosses, or
spins of roulette-in which there is some fixed chance of "winning" each
individual tum (like our variable D). Binomial variance equals the number
of events (n), multiplied by D, multiplied by 1- D.
If you flip a coin 10,000 times you would expect, on average, to get
5,000 tails. The variance is 2,500 and the standard deviation (the square
root of variance) is 50. If there are enough coin flips, the binomial
distribution becomes very close to the normal distribution and its classic
bell curve. About 68.8% of the time (versus 68.3% for a normal
distribution), the result will be 5,000 ± 50 tails, and about 95.6% of the
Probability of Netting 5+ Chips in Roulette
-
20
~ 15
:c~cu 10
.c
e
a.
5
101
201
301
401
501
601
701
801
901
1,001
Number of Spins
If you play for too long your chances will keep declining. D works against you here, because your
chances of winning each spin in roulette are only about 4 7.4% (eighteen of the thirty-eight spaces on
the wheel are red). On the other hand, minimizing your number of spins doesn't help either; winning I 0
or more times out of 15 spins (probability 10.8%) is less likely than winning 160+ out of 315 spins
(probability 12.3%). You need to take enough chances to give yourself a nice-sized variance. The
optimal number of spins is 75 or 77 (probability 17.9%). In a recount, the effect of variance (and thus
the optimal number of chances to take) would be much larger than this; binomial distributions make for
simple illustrations, but they understate the variance in recounts. See infra Part l.B.5.
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Journal ofLaw & Politics
[Vol.XXX: 141
time (95.5% for a normal distribution) it will be 5,000 ± 100 tails. Mildly
extreme results are highly unlikely: getting more than 5,150 tails out of
10,000-three standard deviations above the expected value-has a
probability of only 0.13%.
But voting and recounts are different from coin flips. We cannot assume
that the plain binomial model is appropriate to determine variance, even if
there is a fixed value for D. As an example, take a jurisdiction in which the
challenger lost the initial count by only 20 votes out of 100,000, with no
third-party candidates. Assume that a cache of 75 previously uncounted
votes is discovered. Given that both candidates had essentially equal
support (D equals 49.99%), we might presume ex ante that these new votes
are essentially equally likely to go to either one of them, so that the
challenger could expect to get 37.5 new votes (and no net votes). If we use
the binomial model, the variance for this estimate would be 18.75, and the
standard deviation would be 4.33. The challenger's chances of winning
(getting at least 48 of the new votes, to the defender's 27) would be only
1%, as he or she would need a result that is 2.42 standard deviations above
the expected result.
But now consider what would happen if these 75 new votes were all
from the same precinct. Unless we know which precinct the votes are from,
we probably cannot predict which candidate is likely to benefit more; the
expected value of Vnet is still zero. The variance, however, will probably be
larger. An extreme example makes this point clear. Assume that this
jurisdiction comprises two very large and completely polarized precincts:
one supports the defender 100% (50,010 to 0 in the initial count), and the
other supports the challenger 100% (49,990 to 0 in the initial count). If we
know that all of the votes came from one area or the other, then there is an
almost 50% chance that they came from the challenger's turf. In such a
case, even though the expected value-the average of our expectations-is
still zero, P becomes 50%, obviously much higher than the previous 1%
chance. Instead of having to do the equivalent of winning at least 48 out of
75 coin flips, the challenger now just has to do the equivalent of winning
one.
To be sure, the "clustering" of new votes will rarely, if ever, be this
stark. But anything that causes any sort of clustering will increase the
probability of a more extreme result. Doubling the variance from the first
example, from 18.75 to 37.5, increases P more than fourfold.
Clustering seems inevitable in our example unless each precinct is a
perfect microcosm of the entire jurisdiction. The odds of this occurrence
are slim, however, given the numerous social and economic variables that
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correlate with both voting preference and local geography. Moreover,
ballots may be rejected for reasons that correlate with support for one
candidate or the other. That is, one candidate may have supporters who are
0
more likely to miscast a ballot in a certain way; this increases variance?
There is also the potential for clerical errors that transcend the one-vote-ata-time binomial model, such as transposing digits or mistaking a 6 for a
21
1. Examples abound, and there will be plenty more when this Article
turns to consider the Florida recount. In the abstract, though, without
knowing the nature of these clusters in advance, we must assume that they
are as likely to benefit one candidate as the other; once again, the expected
value of Vnet remains at zero. But the potential for clustering exists and it
raises the variance significantly.
In fact, clustering might make the very concept of variance less salient,
because clustering leads us away from thinking of a recount as a huge
number of independent one-vote coin flips, and more toward thinking of it
as a smaller number of interrelated, multi-vote determinations. In doing so,
it takes us away from the tidy statistical realm of binomial and normal
distributions, bell curves, and ultimately, away from the notion of being
able to calculate or predict variance with any kind of precision.
Some statisticians who analyze voting recognize the clustering effectwith regard to regular voting, let alone the even-more-clumpy area of
voting errors and recounts-and so they use overdispersed binomial
distributions in their analyses, making their variances more than double
what they would be with a regular binomial distribution. 22 However, this
20
The formula for combining the variance of A with the variance of 8 is (Variance A+ Variance 8
+ (2 · Covariance of A & 8)). Covariance is the extent to which the results in the individual
components are interlinked. If voters supporting one candidate might spoil their ballots in similar ways,
it will thus make the total variance greater. The butterfly ballot is a perfect example; it affected Gore
voters but not Bush voters, and thus led to a much larger anti-Gore error than anything neutral and
random could ever have caused. See Jonathan N. Wand et al., The Bullerjly Did It: The Aberrant Vote
for Buchanan in Palm Beach County, Florida, 95 AM. POL. Sci. REV. 793 (2001) (analyzing effect of
butterfly ballot statistically).
21
Just such an error reversed the presidential result in New Mexico in 2000. Gore's absentee vote
total in one district was misread as 120 instead of 620. When that was corrected, Gore gained 500
votes; he ended up winning the state by only 366. See Fritz Thompson, Cowchip Awards 2000,
ALBUQUERQUE J., Jan. I, 200 I, at A I, available at 200 I WLNR 2179971.
22
See, e.g., Walter R. Mebane, Jr. & Jasjeet S. Sekhon, Robust Estimation and Outlier Detection
for Overdispersed Multinomial Models of Count Data, 48 AM. J. POL. SCI. 392 (2004); Wand et al.,
supra note 20; Dennis Gilliland & Paul Meier, The Probability of Reversal in Contested Elections, in
STATISTICS AND THE LAW 391, 398-99 (Morris H. DeGroot et al. eds., 1986). Some, however, have
rejected its use. See, e.g., Michael 0. Finkelstein & Herbert E. Robbins, Mathematical Probability in
Election Challenges, 73 COLUM. L. REV. 241 (1973); Herbert Robbins, Comment on 'The Probability
154
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Article will not delve into more complicated statistical realms. There are
currently no good ways to model rigorously the possible outcomes of a
recount in which there are so many unknown factors. Sometimes caches of
previously uncounted votes will be found; most of the time they will not.
Often there will be errors in data entry or arithmetic that are not caught
right away; often there will not be. Sometimes machine malfunctions will
be uncovered; most of the time they will not. There will often be ballots
that the machines missed but that manual examination will reveal to reflect
a clear choice, and others for which manual examination will set up a
dispute between the parties. But there are few good ways to predict the
results of such recounting in advance. Even in cases in which partial
recounts allow for projections to be made about their remainders, it is often
difficult or impossible to be rigorous about calculating variance. In time,
perhaps, researchers will generate enough data about various types of
errors, various voting technologies, and the ways in which various political
and demographic variables interact with them, that they will be able to
make accurate forecasts of expected value and variance. But that time has
not yet arrived, and pretending that it has only leads to false confidence
and the accompanying errors.
In any case, finding a model to predict precisely the expected value and
variance of a recount is not necessary to make the point that the
challenger's chances of success will be larger, often significantly larger,
than the pure binomial model would suggest. Challengers must take care
not to sell their chances short by underestimating the likelihood of
seemingly extreme results-results that would be extreme were we
flipping coins, that is. 23
Thus, to the point of the previous section-that challengers need to
consider the variance, not just the expected value-we can add another: the
variance may be quite a bit higher than they think. In the previous section,
we saw that challengers should seek to recount votes even when doing so
would reduce the expected value of a recount, so long as doing so would
also raise the variance of that prediction by enough. When using normal
distributions, "by enough" might not be very often, 24 but once we reject the
use of normal distributions it can be very often indeed.
of Reversal in Contested Elections', in STATISTICS AND THE LAW, supra, at 412.
23
See generally NASSIM NICHOLAS TALEB, THE BLACK SWAN (2007) (investigating human
tendency to underestimate the chances of seemingly improbable but highly consequential events).
24
With some algebra and a little calculus (proofs on file with author), we can calculate that the
2014]
Winning Recounts
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6. Reliability
No known vote-counting system is perfect, and a challenger must try
both to estimate the reliability of the initial count and to forecast the
reliability of the recount. The number of virtual votes can be expressed in
terms of the reliability of the counting systems. V equals: (1) miscounted
votes from the first count; plus (2) miscounted votes in the second count;
minus (3) votes that are miscounted the same way in both counts. To be
sure, the term "reliability" may be a misnomer. The first (machine) count
might consistently and appropriately exclude certain votes-say, those in
which the voter made a clear mark but one that was not dark enough for
the machine to pick up-while the second (hand) count might consistently
and appropriately include them. Neither count was "unreliable" in the
layperson's sense of the word, but such a situation will increase Vbecause
the second count will defme all of those lightly marked votes as having
been miscounted in the first count.
Without knowing the expected relative effect of reliability (i.e.,
assuming that D equals 50%), we at least know that the lower reliability is,
the higher V will be. The higher V is, the higher the variance in the
predicted value of Vnet will be, thus improving the challenger's recount
prospects (P). Thinking back to the three components of V in the last
paragraph, then, challengers do better when the first count is unreliable
(maximizing the first term), when the second count is unreliable
(maximizing the second term), or when the reliability of the two counts is
different (minimizing the third term, which is subtracted from the total).
The first count will have been performed already, and so the challenger
can only estimate its reliability and assess things accordingly; the more
unreliable a first count was, the more apt a challenger should be to try to
recount it. Regarding the second count, however, challengers have more
control over the result. They can increase P in two ways. First, they can
seek a recounting method that is as unreliable as possible. This strategy is
not a promising one insofar as it will be difficult to make an effective
public case for it; we presume that the defender will jump to contest it and
that the authorities will be more reluctant to adopt it.
The second method is more promising: seeking a recounting method
that is as different from the initial method as possible, and so minimizing
the number of votes miscounted the same way both times. This approach
optimum n (i.e., the point at which P peaks) for a given M and D will be at or just below M/(1- 2D).
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will be an easier case to make. Challengers can use democratic rhetoric
about ensuring that every vote is counted, which means finding as many
votes as possible that the first counting method missed, which in tum
means using a different way of counting. The benefit to challengers' actual
prospects, though, comes from the increase in Vnet and its variance, not
from satisfying the public's democratic impulses.
7. Legal Probability
The final factor affecting P is L, the probability of turning virtual votes
into actual votes through the legal process. This entails both obtaining a
recount and defming its bounds. It may also encompass litigation in
administrative, trial, and appellate tribunals. While legal probability is very
difficult to estimate precisely, lawyers are used to at least attempting to
make such calculations, usually out of necessity? 5 If a recount is pursued,
there may be disagreement over which votes count as legal votes-the
challenger may wish to count certain types of marks as votes, while the
defender does not. When challengers lose such legal arguments, P drops.
Mathematically, L can either interact with Vnet directly to determine P,
or it can interact with discrete groups of votes to discount Vnet· As an
example of the former, assume that the challenger's recount strategy offers
a 70% chance of yielding a Vnet greater than M, but that implementing that
strategy requires winning a difficult legal argument with only a 10%
chance of success. In such a situation, P equals [L · p(Vnet > M)], or 7%.
In the latter situation, separate legal probabilities can be used to
discount predicted gains in discrete subcategories of recounted votes. If L
equals 10% for a cache of votes in which Vnet equals 50, and is 20% for an
independent cache where Vnet equals 40, then the total expected value of
the two caches is 13 votes (5 + 8). By aggregating all of the individual
expected values (and their variances), the challenger can assess a final
aggregate value of P (and its associated variance)?6
25
A common example is deciding whether to accept a settlement or proceed to trial, which requires
forecasting both the probability and likely magnitude of a victory at trial. See generally Maljorie Anne
McDiarmid, Lawyer Decision Making: The Problem of Prediction, 1992 WIS. L. REV. 1847.
26
Aggregating variance requires considering covariance-the extent to which individual
components vary in unison with each other. See supra note 20.
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8. Summary of Probability
Statistically, the probability of a recount altering the election result (P)
can be expressed as a function of the number of votes being re-examined
(n), the gross and net number of "virtual" votes that are expected to change
(V and Vner), the defender's initial margin of victory (M), the likelihood of
each virtual vote being for the challenger as opposed to the defender (D),
and the legal probability of translating the virtual votes into actual votes
(L).
Through their effect on the expected value of a recount and the variance
associated with that expectation, most of these factors will increase P as
they themselves increase. Increasing Vner, D, and L will boost the expected
value of the recount. Increasing n and V will increase variance, and
therefore generally increase P-often even when D is less than 50%.
Variance will be significantly higher than that suggested by a simple
binomial (coin flip) model, because of the potential "clustering" of new
votes.
The challenger can also increase V by obtaining recounting methods
that are as different from the initial counting method as possible.
Obviously, the last remaining variable, M, will decrease P as it increases;
the farther behind challengers start out, the lower their chances are of
winning a recount.
9. Other Benefits and Costs
So far in this Article, the only benefit of a recount for the challenger
discussed is that it might reverse the election result, and costs have largely
been ignored. A recount may offer other benefits, however, and will
present costs as well.
One benefit is that a recount, even if unsuccessful for the challenger,
may have emotional "process value." That is, it may make challengers and
their supporters feel better about losing-as opposed to the ill feeling of
helpless surrender, or the nagging sense that they might have won had the
votes been re-examined. There may also be political value in seeking a
recount; a candidate might wish to fight for accuracy and efficiency in the
electoral process, consistent with a platform of honest and efficient
governance. A candidate might also wish to highlight systematic
imbalances in the errors in the first count, consistent with a platform of
equal rights and justice. (In the latter two cases, this political value might
be satisfied largely by the challenger making those arguments rather than
actually winning them.)
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Recounts entail costs as well. In some situations under certain state
statutes, a challenger must front the administrative costs incurred by
election officials. 27 Additionally, sponsoring the lawyers and other
partisans who represent the challenger on the ground is also potentially
expensive. There may also be political costs. If the recount fails, the
challenger may jettison a politically lucrative perception that he or she was
the true winner. Win or lose, the request may give him or her a reputation
as a sore loser or a cheater; it may be better to appear (publicly) highminded, concede defeat, and try again next time. 28 The less likely the
challenger is to win, the higher these costs will be.
Partial recounts may affect other costs and benefits as well. The
additional legal argument and effort needed to distinguish and subdivide a
mass of votes may exceed the savings from the smaller counting effort. In
terms of political costs, a less-than-complete count may sacrifice the moral
high ground, and could fuel a perception that a challenger is engaging in
unseemly strategic behavior.
These sorts of calculations will vary among the infinite possible factual
contexts, so attempting to be systematic about them, let alone to quantify
them, is pointless in a venue such as this. Nevertheless, it seems that a
challenger will typically have much more to gain than to lose. In an age of
short voter memory, the high stakes of a political race almost certainly
ensure that the benefit of winning a recount will exceed the net cost of
making the attempt, so long as the challenger has a real chance of reversing
the election result. It might hurt to be called a sore loser or a cheat, but
winning a recount and taking office would tend to take a lot of the sting out
of it. 29
C. Defenders
This Article has not considered defenders so far, for the simple reason
that defenders will rarely want to sacrifice the 100% chance of winning
27
See, e.g., MICH. COMP. LAWS ANN.§ 168.881(1) (West 2005).
See TAPPER, supra note 4, at 93 (discussing Nixon's decision not to contest the 1960 presidential
election); Chris Cillizza, Losing by a Hair, CAMPAIGNS & ELECTIONS, June I, 2005, at 21 (discussing
other such candidates).
29
Gore apparently remarked, when rejecting his aides' advice to challenge questionable military
absentee ballots, "If I won this thing by a handful of military ballots, I would be hounded by
Republicans and the press every day of my presidency and it wouldn't be worth having." David
Barstow & Don VanNatta Jr., How Bush Took Florida; Mining the Overseas Absentee Vote, N.Y.
TIMES, July 15,2001, at I. One wonders if Gore still felt that way in 2004 or 2008.
28
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159
they would have in the absence of a recount. However, defenders may not
succeed in preventing a recount, and thus may need to bolster their position
or even plan as if they are the underdogs. Conversely, challengers may
have such a good chance of prevailing that they essentially become
defenders.
The flip side of the challenger's strategy-a challenger should seek to
add a group of votes to a recount when doing so will increase expected
value or when it will decrease expected value but provide a large enough
increase in variance-is that a defender should seek to recount a group of
votes only when doing so will increase expected value and avoid much of
an increase in variance. A defender who is reasonably certain of winning
thus will not want to choose any recount options unless their expected
value to him or her is positive (or close to it) and their variance is low.
Thus, a defender should fight to keep Vner. D, and L low, and obtain
recounting methods that are as close to the initial counting method as
possible.
In summary, challengers should seek to recount even those votes they
expect to cut against them, so long as that expectation is sufficiently
uncertain. Defenders should seek to avoid recounting even those votes they
expect to favor them, unless that expectation is sufficiently certain.
If ever a defender feels that he or she is more likely than not to lose,
however, then he or she is in the same position as an underdog challenger,
and should seek additional recount options with positive expected values
or high variances.
D. Tim Downs and The Recount Primer
The Recount Primer (the "Primer") 30 is a book by Democratic recount
experts Timothy Downs, Chris Sautter, and John Hardin Young. The three
worked for Gore during the recount, and they brought the book with them
to help train Gore operatives as they flew to Florida after Election Night to
fight for their candidate. 31 In their lengthy careers, the authors had fought
recount battles both as challengers and defenders; the strategies set out in
the Primer were just as valuable for Republicans as for Democrats in 2000.
The book is filled with valuable advice about effectively managing the nuts
and bolts of actual recounts. It also provides the conventional wisdom on
30
31
DOWNS ET AL., supra note I.
See TOOBIN, supra note 5, at 28.
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strategy. That conventional wisdom is consistent with the mathematical
principles in this Article.
The Primer says that for defenders, "the scope of the recount should be
as narrow as possible, and the rules and procedures of the recount should
be the same as those used election night." 32 To recount as little as possible
is, as this Article puts it, to minimize n and V. 33 To use standards as close
to those used in the first count is to maximize reliability. 34
The Primer's strategy for challengers tracks the mathematical principles
of this paper as well: "If a candidate is behind, the scope should be as
broad as possible, and the rules for the recount should be different from
those used election night." 35 This rule maximizes n and V and minimizes
reliability.
Elaborating on the idea of recounting as broadly as possible, Downs
clarified later that a challenger should exclude only those votes for which
there are concrete facts to indicate that a recount will cause a drop in votes
(unfavorable expected value and low variance). 36 Downs did not say to
avoid recounting votes that challengers think will hurt them, but only to
avoid recounting those that they fairly know will hurt them. If the variance
of the predicted results of a group of votes is high enough, merely thinking
that they probably lose votes for the challenger is not enough of a reason to
avoid recounting them. Moreover, as discussed above, variance will often
be much higher than simple binomial models might suggest/ 7 giving the
challenger a reason to assume a higher variance and err on the side of
including more votes in a recount.
II. THE FLORIDA 2000 RECOUNT
This Part of the Article will briefly summarize what happened in the
2000 Florida recount, putting some of it in terms of the variables discussed
in the last section. It will then analyze how the choices made by AI Gore's
team (and to a lesser extent, George W. Bush's) compare to the optimal
strategy.
32
DOWNS ET AL., supra note I, at 5.
See supra Part 1.8.3.
34
See supra Part 1.8.6.
35
DOWNS ET AL., supra note I, at 5.
36
Timothy Downs, Tim Downs Tells about Recent Recount Efforts in Florida, INGHAM COUNTY
BAR BRIEFS, Feb. 2001, at I.
37
See supra Part 1.8.5.
33
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A. What Happenecf8
1. The First Count and the Automatic Recount
On election night, November 7, major media outlets initially called
Florida for Al Gore. Then they retracted that, classifying it as too close to
call. In the wee hours of the following morning, the media called Floridaand with it the presidency-for George W. Bush. Then they retracted that,
classifying Florida once more as too close to call. It would remain so for
more than a month. 39
The first set of complete returns announced on November 8 showed
George W. Bush with 2,909,135 votes to AI Gore's 2,907,351. Other
candidates received about 138,000 votes. An additional group of almost
180,000 votes, an embarrassing 3% of the total, went to nobody, at least as
far as the machines performing the first count were concerned. This
included both invalid "undervotes" on which the machines detected no
choice, and invalid "overvotes" on which the machines detected more than
one choice. Bush's lead-1,784 votes, or 0.03%-was a mere hundredth of
this number of rejected ballots. (An Appendix with a complete reckoning
of the county and state totals at each stage of the process, and a count of
rejected ballots, appears at the end of this Article.)
In any race decided by a margin of less than 0.5%, Florida law provided
for a state-wide automatic recount. 40 Six days of recounting shrunk Bush's
lead considerably. That result exemplified the "clustering effect" discussed
in Part I.B.5; although the automatic recount caused thousands of votes to
change, the net changes were +1,357 for Bush and +2,841 for Gore-a
pro-Gore ratio that would have been unthinkable if this had been the result
of independently flipping 4,200 coins rather than re-examining millions of
votes. 41
There were multiple "clusters" at play. In 2000, each Florida county
chose its own voting method and had independent discretion over how to
38
For the sake of convenience, this Article cites to a small subset of sources to document the
events of the recount: TAPPER, supra note 4; TOOBIN, supra note 5; and Bickerstaff, supra note 6. The
events of the recount are so well documented, however, that there are numerous other worthy sources
that could have been cited instead. Also, some of the footnotes in this section will come at the end of a
paragraph and cover the entire paragraph, in lieu of having numerous identical citations for each
sentence.
39
See TOO BIN, supra note 5, at 18-20 (initial calls); TAPPER, supra note 4, at 39 (final retraction).
4
FLA. STAT.§ 102.141(4) (2000) (current amended version at FLA. STAT.§ 102.141(7) (2014)).
41
See Joe Follick, Power of Discretion, TAMPA TRIB., Nov. 15, 2000, at I, available at 2000
WLNR 622276 (providing automatic-recount vote change totals).
°
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interpret the automatic recount law. Practices varied. Some counties did
not touch their ballots and just checked their equipment and re-tallied the
precinct-level numbers. 42 Most of these counties showed insignificant
43
changes, if any, although Bush picked up over 100 net votes in Martin
44
when a transcription error there was corrected.
Other counties ran every ballot back through the tabulating machines. 45
This method changed the totals in some counties substantially, most
sizably when groups of ballots were discovered to have been misplaced or
double-counted in the initial tally. This phenomenon provided a huge gain
to Gore-and yet another one that would have been staggeringly
improbable without the clustering effect. For example, Gore won big when
previously uncounted or double-counted votes were straightened out in
46
47
Palm Beach (Gore 510, Bush 99), and Pinellas (Gore 417, Bush -61 ),
while Bush had smaller such gains in Polk (net for Bush of 90), Seminole
(98), and Volusia (58). 48
Changes in the automatic recount in punch-card counties were also
attributed to falling chads: loose pieces of chad that fell off of punch cards
between the first and second counts, causing some ballots to go from being
undervotes to actual votes, and others to go from actual votes to
overvotes. 49 In some places, however, the changes favored Gore so
42
TOO BIN, supra note 5, at 66 (decrying failure of some counties to actually recount ballots); Lisa
Getter, Ballot Recount: Many Things to Many People, L.A. TIMES, Nov. 15, 2000, at I (describing
variation in county practices for automatic recount).
43
To be more concise, I will refer to all Florida counties only by their name (e.g., "Martin" rather
than "Martin County").
44
See Melissa E. Holsman, Gore Narrows Lead, STUART NEWS (Stuart, Fla.), Nov. 10, 2000, at
A I, available at 2000 WLNR 7606774 (describing corrections of errors in Martin County).
45
See Getter, supra note 42 (describing variation in county practices for automatic recount).
46
This total is based on my own analysis of the precinct-by-precinct results in the initial count and
the automatic recount, obtained from Palm Beach County, and a phone conversation on July 5, 2001,
with Theresa LePore, Supervisor of Elections for Palm Beach County. Precinct 29E was overlooked on
election night; when added in it went 368-23 for Gore. According to LePore, Precinct A038, a
grouping of absentee ballots, found a similarly overlooked cache. When counted, it favored Gore 14276.
47
See Rob Shaw, More Than 2,000 Votes Mishandled in Pinellas, TAMPA TRIB., Nov. 10, 2000, at
12, available at2000 WLNR 666290 (describing non-counting of 1,326 ballots and double counting of
739 others). While the biggest changes came from these corrections, there were likely other smaller
changes as well.
48
TAPPER, supra note 4, at 141, 143 (discussing Bush gains in Polk, Seminole, and Volusia from
fixing double-counted precincts). The totals for each county, which are listed in the Appendix, reflect
other changes as well.
49
See Seth Borenstein, On "Chads," Recounts and Ballots, PHILA. INQUIRER, Nov. II, 2000, at
Al9, available at2000 WLNR 2438546 (discussing falling chad phenomenon).
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disproportionately that they cannot have come from such a random
phenomenon. In Palm Beach, for instance, Gore had a 277-6 advantage in
new votes other than those from the discovery of large groups of
previously uncounted votes-the product of separate, slight changes spread
over hundreds of precincts. 50 In Duval, a county that Bush had won on
election night, Gore won 184-16 among the new votes. 51 The odds of such
results arising out of a series of individual, random, independent changes
are preposterously small. Some phenomena other than falling chads must
have been at play. 52
Some counties that used scan ballots used the automatic recount as an
opportunity to do hand counting. 53 For instance, Gore netted 64 votes
(1 05-41) in Orange when county officials, examining ballots by hand,
50
Subtracting the changes from the two precincts with previously uncounted votes from the total
change from the automatic recount of787 for Gore and 105 for Bush yields the 277-6 figure. See supra
note 46. There may also have been double counting in Precinct 194, which changed -II for Gore and -4
for Bush; if so, that would make the total 288-10, a less stark but still very unbalanced number. In my
conversation with her on July 5, 2001, Palm Beach Supervisor of Elections Theresa LePore had no
explanation for the fact that the numerous small changes in hundreds of precincts favored Gore so
heavily. Gore lost ground in a total of 17 precincts, Bush in 39. Gore gained in 168; Bush in 46. Gore
broke even in 453; Bush in 563.
51
See E-mail from Dick Carlberg, Duval County Assistant Supervisor of Elections, to author (May
23, 2001) (on file with author) ("The additional votes for Bush and Gore were most likely due to chad
falling off partially punched holes. In recounts this is the norm. Valid votes for all candidates tend to
increase, undervotes decrease, and overvotes increase. I don't know why the gain heavily favored
Gore."). The changes in vote totals from the automatic recount are detailed in the Appendix.
52
Some rough calculations show just how clear the numbers are here. Assume that the only thing
happening here is that the chad on the ballots was punched such that it was intact the first time through
the machine, but was gone the second time through. Assume further that there is nothing making a
Gore voter more likely than a Bush voter to punch the chad this way. At the county level, this would
mean that if Gore won X% of the county-wide vote in the initial count, a new vote from falling chad
would have an X% probability of being for Gore.
In Palm Beach, Gore won 63.814% of the two-party vote in the initial count. There were 283 new
votes supposedly from falling chad. The probability of winning 277 (as Gore did) or more out of 283,
of
winning
each
one
was
63.814%,
is
less
than
when
the
probability
0.000000000000000000000000000002%. Even if Gore had won 95% of the two-party vote in the
initial count, the chances of a pickup that lopsided would have been only about 1%. Gore's pickup in
Duval was less lopsided at 184-16, but he had won just 41.474% of the two-party vote in the initial
count there. The probability of a 184-16 pickup from falling chad, when the probability for each vote
was 41.474%, is 0.0000000000000000000000000000000000000000000000335%. In other words, the
assumptions that began this exercise can safely be rejected. These new votes for Gore were due to
something other than random fluctuations of chad. Just exactly what remains unclear to this day.
Falling chad also cannot explain changes like that in Palm Beach Precinct 137, to take just one
weird example among many, many of them. In the automatic recount, one more ballot was counted
than in the initial count. Bush's total dropped by two, and the totals for Gore, Harry Browne, and
undervotes each rose by one. Falling chad cannot account for that.
53
See, e.g., TAPPER, supra note 4, at 72 (describing events in Gadsden).
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added votes where the voter (apparently taking the phrase "write in" as a
command) had chosen a candidate and then re-voted for the same
candidate as a write-in. 54 These "redundant write-ins" were rejected by the
machines as impermissible "overvotes," but officials included them as
evincing clear intent. Officials in Gadsden found 187 clear-intent but
machine-rejected ballots, mostly overvotes such as redundant write-ins;
they favored Gore 170-17, netting him 153 votes. 55 Once again, Gore won
tremendously disproportionate gains among these new votes because his
supporters were apparently more likely to make this particular error. Gore
won Orange County by only 50% to 48%, but the redundant write-ins
favored him 72% to 28%. Gadsden went for Gore by 66% to 32%, a far cry
from the 10: 1 advantage he enjoyed among the new votes there.
As a result of all this, the automatic recount helped Gore considerably.
56
By Thursday, Bush's lead had apparently shrunk to 327 votes. Volusia
County's counting process was so confused that Gore asked for and
received a full hand recount there. 57 By November 14, after other counties
updated their numbers and Volusia finished its recount, Bush's lead was
down to 300 votes. 58
B. The Protest Phase
Florida law offered a confusing tangle of recount procedures subject to
varying interpretation. The Bush legal position, supported in large part by
Florida's Republican Secretary of State, Katherine Harris, portrayed the
law as providing a relatively simple process that made it unlikely that
many votes would be recounted beyond the automatic recount: After
election night, each party had three days to "protest" the count in each
county by showing significant problems with the county's voting
machinery or the arithmetic of its election workers. Each county would
decide for itself whether and how to perform a hand recount. The results
from each county would have to be certified on November 14. Because of
a settlement in a federal lawsuit, absentee votes from overseas could come
54
Scott Maxwell & David Damron, Now Democrats Are Upset with the Way Lake Counted,
ORLANDO SENTINEL, Nov. 14,2000, at Al3 (describing Orange debacle).
55
Mary Ellen Klas, N. Florida County Tries to Fill in Blanks on Ballots, PALM BEACH POST, Nov.
10, 2000, at 16A (describing Gadsden process). This characterization of the Gadsden recount is also
based on a discussion I had with Gadsden Supervisor of Elections Shirley Knight in May 200 I.
56
See TOOBIN, supra note 5, at 67.
51
See id. at 38-39, 83.
58
See TAPPER, supra note 4, at 183.
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Winning Recounts
165
in until November 17; when they had, the final results would be submitted
to Harris, who would certify a winner. Once the winner was certified, the
loser could "contest" the result in a single unified proceeding. The winner
after that would get all of the state's 25 electoral votes. 59
The Gore legal position differed in two important respects. First, Gore
argued that counties should conduct hand recounts if the machines, even if
working as intended, had nevertheless rejected a significant number of
votes. On this basis, Gore "protested" and asked on November 9 for hand
recounts in Broward, Miami-Dade, and Palm Beach. 60 These counties-the
"Big 3"-represented over a third of his votes in the initial count, and were
three of the four counties with the largest absolute number of rejected
ballots. (The fourth, Duval, was carried by Bush, 57% to 41%.)
Second, because the November 14 deadline imposed by Harris would
have made it difficult or impossible for the Big 3 to complete their hand
recounts on time, Gore argued in court that there really was no November
14 deadline for protest recounts to conclude. 61 While the three counties
debated how to proceed and the courts wrestled with the deadline question,
Gore made his only gesture-a halfhearted one-toward actually counting
every vote. In a nationally televised address, Gore continued to press for
hand recounts only in the Big 3, but said that "if Governor Bush prefers,"
Gore would abide by the results of a statewide hand recount. 62
Unsurprisingly, Bush did not prefer a statewide recount, and Gore never
asked any Florida officials for one-they, not Bush, were the proper forum
for such a request.
Eventually, the Florida Supreme Court extended the protest recount
deadline to November 26, giving the Big 3 more time to recount. 63 In
obtaining this extension, however, Gore essentially conceded that
December 12 was the deadline for fmishing the "contest" phase, which
would later make the contest proceedings rushed and more difficult. 64
59
For a summary of Bush's interpretation of the law, see Lynne H. Rambo, The Lawyers' Role in
Selecting the President: A Complete Legal History of the 2000 Election, 8 TEX. WESLEYAN L. REV.
I 05, 177-82 (2002).
60
For a summary of Gore's interpretation of the law, see id. at 174-76. The final decision to focus
on the Big 3 (plus Volusia) is described in TAPPER, supra note 4, at 68.
61
See Bickerstaff, supra note 6, at 183.
62
TAPPER, supra note 4, at 190.
63
Palm Beach Cnty. Canvassing Bd. v. Harris, 772 So. 2d 1220, 1240 (Fla. 2000).
64
TAPPER, supra note 4, at 233; TOOBIN, supra note 5, at 134; Bickerstaff, supra note 6, at 199.
Under federal law (3 U.S.C. § 5), a state's result is presumptively valid if it is reached by December 12
and according to pre-existing state law. See 3 U.S.C. § 5 (2012) (in force in 2000 election). If not,
166
Journal ofLaw & Politics
[Vol.XXX:l41
Broward completed its recount on time, netting Gore 567 votes. 65 Palm
Beach fell ninety minutes short of finishing its recount by 5 p.m. on the
26th and so Harris did not accept its new numbers (Palm Beach's haste
meant that the would-be results-176 net votes for Gore-were not known
for a few days and remained disputed). 66 Miami-Dade had begun a hand
recount, but got through only about one-sixth of the ballots before it
concluded that it could not finish in time and stopped. Gore's gain in
Miami-Dade's partial count was 168. 67
Unfortunately for Gore, the 567 net votes from Broward were not
enough to overcome Bush's lead, which had grown from 300 to 930 on
November 18 after the late overseas absentee ballots were added in. 68
Additionally, several other counties took advantage of the November 26
extension to adjust their totals. First, Bush netted 51 votes when Nassau
County, having discovered that it omitted a group of votes in the automatic
recount, reverted to the prior, more inclusive count. 69 Second, Bush's team
made a special effort (discussed in more detail later70 ) to have several
counties reconsider overseas absentee ballots that it had rejected for things
like missing postmarks; that initiative netted Bush over a hundred more net
votes. Harris thus certified Bush's lead on November 26 at 537 votes. 71
C. The Contest
Having been certified the loser, Gore contested the result, seeking five
separate actions:
(1) Nassau to return to its second, smaller count. Net gain: 51. 72
(2) The tardy Palm Beach results to be included. Net gain: either 176 or
215. 73
Congress would have been allowed to question and reject the state's electoral votes much more easily
when it tallied them in January.
65
See TAPPER, supra note 4, at 3 15.
66
See Bickerstaff, supra note 6, at 186 & n.l52.
67
See id. at 187-88 (describing Miami-Dade experience).
68
See TOOBIN, supra note 5, at 124.
69
See TAPPER, supra note 4, at 308.
70
See infra text accompanying notes 102-05.
71
See TOOBIN, supra note 5, at 189. A full reckoning of these changes appears in the Appendix.
72
See Gore v. Harris, 772 So. 2d 1243, 1248 (Fla. 2000) (reciting Gore's claims), rev'd sub nom.
Bush v. Gore, 531 U.S. 98 (2000).
73
See id. at 1248 (reciting Gore's claims). Bush claimed the true number was 176. See id. at 1248
n.6. Gore claimed it was 215 and the county canvassing board reported the number as 174. See Brad
Hahn, Yo-Yo Totals Cause ConfUsion In All, Four Totals Surface For Gore, SOUTH FLORIDA SUNSENTINEL, Dec. 10, 2000, at !SA, available at 2000 WLNR 8527331 (describing confusion over
2014]
Winning Recounts
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(3) The partial Miami-Dade recount to be included. Net gain: 168. 74
(4) The rest of Miami-Dade's "undervotes" to be hand counted. Rather
than examine all 512,790 of the ballots left out of the aborted hand recount,
Gore wanted to speed things along by focusing just on the 9,000-or-so
undervotes. Gore estimated to the court that this count would net him 600
votes. 75
(5) The Palm Beach recount standards to be expanded to include socalled dimpled chad (punch card ballots in which a selection had been
dimpled but not detached from any comers). Palm Beach had counted
dimples only in the rare case where the voter had left similar dimples for
other races on the ballot. If the court used the more lenient standard to
count the Palm Beach ballots, Gore argued, he would net 800 more votes
there. 76
The trial court rejected all of Gore's claims, and Gore appealed. The
Florida Supreme Court affirmed the rejection of Gore's first (Nassau) and
fifth (Palm Beach dimples) claims, but it reversed the trial court on the
other three. It ordered the inclusion of Palm Beach's net 176 or 215 votes
(directing the lower court to find the proper number) and the 168 net votes
from the partial Miami-Dade count. This dropped Bush's lead down to 154
or 193 votes. It also ordered that the undervotes in the remainder of MiamiDade be hand counted. 77
If the Florida Supreme Court had stopped there, things would have been
very different. First of all, Gore would have lost, and lost quickly. The
remainder of Miami-Dade held no hope for Gore; as discussed later, his
estimate to the court that it would yield him many votes, let alone 600 of
them, was fanciful. 78
Second and more significant, though, the Florida Supreme Court
ordered a recount that Gore had not sought-that his lawyers had in fact
argued againse 9-but that was more along the lines of Gore's "Count
various counts in Palm Beach). The courts and parties, however, seem to have ignored the 174 figure.
74
See Gore, 772 So. 2d at 1248 (reciting Gore's claims).
75
See Complaint to Contest Election at 4, Gore v. Harris, No. 00-2808, 2000 WL 1770257 (Fla.
Cir. Ct. Dec. 4, 2000), available at http://www.jurist.law.pitt.edu/election/CV-00-2808a.pdf (last
visited Feb. 28, 2014), rev 'd, 772 So. 2d 1243 (Fla. 2000), rev 'd sub nom. Bush v. Gore, 531 U.S. 98
(2000).
76
See id. at 3-4.
77
Gore, 772 So. 2d at 1258-61.
78
See infra notes 114-15 and accompanying text.
79
See, e.g., TAPPER, supra note 4, at 412, 414 (recounting David Boies's argument to Florida
Supreme Court on behalf of Gore).
168
Journal of Law & Politics
[Vol.XXX:l41
Every Vote" slogan. The court ordered hand counting of all of the
undervotes in the entire state not already counted (i.e., excluding Volusia,
Broward, Palm Beach, and one-sixth ofMiami-Dade). 80
The counties began separating out and counting their undervotes. Some
were apparently going to reexamine overvotes as well. 81 However, the U.S.
Supreme Court stopped them on grounds that the lack of a single statewide
standard for interpreting ambiguous votes was unconstitutional. 82 With
further recounts off the table, Gore conceded and Bush's victory was
finalized at a 537-vote margin. 83
D. Assessing Gore's and Bush's Strategies
This section applies the precepts of optimal recount strategy developed
in Part I to the facts on the ground in the Florida recount set out in Part II,
sections A-C. Put another way, it describes in mathematical terms where
Gore went wrong.
1. The Automatic Recount
As discussed above, 84 Florida Statutes § 102.141(4) provided for a
state-wide automatic recount in any race decided by a margin of less than
0.5%, and the margin the morning after the election was only 0.03%. The
statute did allow the losing candidate to request otherwise, 85 but Gore
made the obvious and correct call by declining to do so.
The automatic recount produced gains that sharply favored Gore, but it
produced an even greater benefit for him for later use: information. Gore's
team may have been impressed by the huge and disproportionate gains
they won in the punch-card counties, 86 but they should have also taken note
of the significant and disproportionate gains they won from other sources,
like redundant write-ins and other overvotes. This information was neither
secret nor obscure. Orange and Gadsden demonstrated in the first days of
80
Gore, 772 So. 2d at 1262.
See 67 Counties 67 Recounts, ST. PETERSBURG TIMES, Nov. 12, 2001, at 6x, available at 2001
WLNR 11081956 (listing nine counties that indicated they would have counted overvotes).
82
Bush v. Gore, 531 U.S. 98, 109 (2000).
83
See TOOBIN, supra note 5, at 268-70 (recounting Gore's concession).
84
See supra Part li.A.l.
85
The statute provided that "[a] recount need not be ordered with respect to the returns for any
office, however, if the candidate or candidates defeated or eliminated from contention for such
office ... request in writing that a recount not be made." FLA. STAT. § 102.141(4) (2000) (current,
amended version at FLA. STAT.§ 102.141(7) (2014)).
86
See supra text accompanying notes 50-52.
81
2014]
Winning Recounts
169
this whole drama that scan ballots and overvotes in counties outside the
Big 3 were a potentially rich source of new net votes for Gore. 87 Gore's
team knew it but did not want to take the risk and decided to focus instead
on punch cards in the Big 3. 88
2. The Protest Phase
Even before the automatic recount concluded, Gore needed to decide on
a strategy for the protest phase. He considered three such strategies, each
promoted by a different faction among his advisers. 89 One option was to try
to protest the results in all sixty-seven counties and thereby obtain what
would amount to a statewide hand recount. This choice was pushed by the
Gore team's recount veterans, Tim Downs, Chris Sautter, and John Hardin
Young, the authors of The Recount Primer. Their strategy (in terms that
this Article has used) was to seek out the highest possible n and V, and
highest possible variance, and then let the chips fall where they may. Not
only would this have been the sensible choice from the standpoint of the
mathematics of recounting, it also would have tracked Gore's slogan of
"Count Every Vote."
Others on the Gore team disagreed. The protest procedure was
decentralized. As such, a siatewide recount would have meant making
sixty-seven separate and possibly unsuccessful recount requests, and
fighting legal battles in sixty-seven different courts. A better alternative,
they argued, was to skip the protest phase and go quickly to the centralized
contest procedure, where a comprehensive statewide recount would be
easier to manage. A statewide recount, even a delayed one, would provide
a high n, V, and variance, and would have been consistent with a slogan of
"Count Every Vote."
A third faction rejected the idea of a statewide recount altogether. Time
was of the essence, and political standing was as important in the short
term-to this faction anyway-as any abstract strategy. Therefore, this
faction argued in favor of limited recounts, in those counties that the
sketchy data available showed as offering the best chance to quickly add
87
See supra text accompanying notes 53-55.
See TAPPER, supra note 4, at 184-85 (describing deliberations); see also id. at 134 (describing
Gore's recount expert Jack Young handling redundant write-ins in Volusia recount).
89
The contents of these deliberations have been widely reported. See, e.g., WASHINGTON POST,
supra note 5, at 77-79; TAPPER, supra note 4, at 66--68; TOOBIN, supra note 5, at 37-39. These sources
provide support for the descriptions in this paragraph and the two that follow.
88
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Journal of Law & Politics
[Vol.XXX: 141
votes to Gore's column. Gore would not be able to continue a recount
effort without political support, they argued, for which he would require
rapid and substantial gains from a focused attack rather than a scattershot
one. This group thus sought to maximize D at the expense of higher n, V,
and variance.
Ultimately, the third faction won Gore over. Indeed, throughout the
recount, Gore favored his political advisors over his recount experts. 90
Following the third faction's advice, Gore sought hand recounts just in
Volusia and the Big 3 (Broward, Miami-Dade, and Palm Beach).
The Big 3 were not only the largest counties in Florida, they were also
the most pro-Gore in terms of his net margin of victory on election night.
They each used punch-card ballots; given both punch cards' well-known
unreliability and the gains Gore reaped from them during the automatic
recount, Gore's team probably thought that they were the most lucrative
potential source of additional votes. 91 Another punch-card county, Duval,
had almost as many rejected ballots as Miami-Dade and Palm Beach, and
many more than Broward. However, Duval also favored Bush by 17%.
Gore's goal was not to count every vote, it was to win, so Duval was off
his list. 92
Some numbers make clear just how rich a lode the Big 3 must have
appeared. Multiplying the number of rejected ballots in each county by
Gore's percentage of victory there provides a crude estimate of each
county's relative prospects. For instance, if Gore won a county 60% to
40% and there were 1000 rejected ballots there, the prospect number would
be 200---ten times as high as in a 60-40 county with 100 rejected ballots,
or a 51-49 county with 1000 rejected ballots. The prospect number for the
Big 3 was about +15,000 for Gore. The other pro-Gore counties together
were under a thousand. The pro-Bush counties were almost -14,000. 93 If
only the Big 3 were recounted, if the new votes came in the same
proportions as the old votes, and if 10% of the rejected ballots turned into
90
See TOOBIN, supra note 5, at 29, 83, 165; Bickerstaff, supra note 6, at 169 (describing absence of
recount expertise among Gore's top decision makers). Cf id. at 206 (attributing relative success of
Bush's legal effort to his divided delegation oflegal and political responsibilities).
91
See TAPPER, supra note 4, at 61-62, 65--68 (discussing awareness of problems with punch-cards
and Gore strategizing).
92
It may also be that Gore's team was misinformed early on about the number of rejected ballots in
Duval. See Bickerstaff, supra note 6, at 169.
93
County-level vote margins (from which initial vote margins can be approximated) and numbers
of rejected ballots appear in the Appendix.
2014]
Winning Recounts
171
new votes upon reinspection, the Gore camp could reasonably expect to
pick up over 1500 votes and win the election.
All of these counties also had canvassing boards controlled by
Democrats. County canvassing boards had significant independent
discretion under the Florida system. 94 Gore might have expected that such
officials would be more sympathetic to his cause, thereby making it more
likely that he would be able to obtain the recounts he wanted in the manner
he wanted. 95
Whatever sense the third faction's strategy made in the fog of the first
days after election night, however, choosing it was to prove a fatal error.
By focusing on the messy and difficult-to-interpret punch cards, Gore
sacrificed the benefits of a quick count. By focusing just on the Big 3, Gore
took on the drawbacks of a limited count. His recount experts knew better;
for a challenger, opening up additional cans of worms is a good thing. 96 It
also had political drawbacks, allowing Bush's team to portray Gore as a
cherry-picker bent on stealing the election. 97
To be fair, Gore had only limited information before the seventy-twohour deadline for requesting hand recounts expired. 98 He was facing
tremendous political costs. He did not know how long sixty-seven separate
protests wouid take. The law was not well-settled. Perhaps Gore and his
team were simply convinced that they had won more votes, if only they
could get them counted. But to the extent that this conclusion was based on
irretrievable votes (that is, those for which L was zero or close to it) such
as those lost to the butterfly ballot,99 it was an irrational one. Moreover,
given the incredibly complex and rapidly changing factual landscape, it
was risky to come to any conclusions with such assurance.
To the extent, however, that Gore thought that he could obtain several
hundred net votes from the 28,000 undervotes in the Big 3 counties, where
local officials were all Democrats, and where he had won in the first count
by more than a 22% margin, his calculations may have made a sort of
94
See Rambo, supra note 59, at 121 (analyzing statutory basis of individual counties' discretion
over manual-recount requests).
95
Cf TAPPER, supra note 4, at 66 (detailing Gore team's concerns about cooperativeness of
officials in Republican counties).
96
See supra Part I. D.
97
See TAPPER, supra note 4, at 345; Bickerstaff, supra note 6, at 178.
98
Compared to Bush, Gore also had fewer lawyers fanned out across all 67 counties. See
Bickerstaff, supra note 6, at 168.
99
See supra text accompanying note 12.
172
Journal ofLaw & Politics
[Vol.XXX:141
sense. If he concluded that his P exceeded 50% in such a cherry-picked
recount, it would have been appropriate for him to adopt the posture of a
recount defender rather than a challenger. As a defender, he would want to
exclude not only those protests where he could expect to lose ground, but
even those where gaining ground would come at the cost of unduly
increasing variance.
That said, Gore's choice made no sense on its own terms. If the idea
was to reap big gains quickly, focusing on punch-card ballots in huge
counties was probably the worst way to do it. Because counties would
recount individually during the protest phase, they would be working in
parallel. The time that a recount would take, therefore, would be based on
whichever county would be the slowest. Gore's three counties were
Florida's largest, with the most votes to recount. Moreover, hand counting
punch cards is slow business. The Florida Supreme Court's extension of
the protest deadline to November 26 allowed each of the three counties to
attempt a hand recount, but during the time it took to conduct the threecounty recount, every other county would have had plenty of time to
conduct its own. It would have taken more effort, and more partisans on
the ground, but it most certainly would not have taken more time. 100 Most
of these other counties favored Bush, and many of them rejected ballots at
a higher rate than the Big 3, two things that would have lent valuable
legitimacy to a recount request from Gore.
For their part, Bush's team apparently made a different calculation of
the P represented by Gore's four-county recount. If he had concluded that
Gore's P was greater than 50% (considering the odds both in court and at
the counting tables), then Bush would have behaved like a challenger
instead of a defender and broadly sought out recounts of his own. Rather
than let Gore cherry-pick unopposed, Bush could have targeted the
counties that apparently formed his own richest lode. 101
Instead of countering Gore, though, Bush's team focused its energies
elsewhere: overseas ballots. Specifically, the Bush team fought to include a
subset of the overseas absentee ballots that initially had been rejected for
100
See Steve Bickerstaff, Counts. Recounts. and Election Contests: Lessons from the Florida
Presidential Election, 29 FLA. ST. U. L. REV. 425, 465 n.211 (2001) (vouching, based on personal
experience, for the feasibility of filing timely challenges in each county).
101
Cf Bickerstaff, supra note 6, at 177-78 (describing Gore team's incorrect-but not
unreasonable-assumption that Bush would respond to Gore's cherry picking with recount requests of
his own); see supra note 18 (describing Rogers-Byrum recount in 2000).
2014]
Winning Recounts
173
lack of a postmark or other authentication-this notwithstanding Bush's
efforts elsewhere to keep n low by insisting on strict adherence to rules and
denigrating recounts. 102 Overseas absentee ballots that had not been
rejected favored Bush 1380-750, 103 so this was fertile ground. Through
careful collection of data Bush's team was able to discriminate further and
predict which individual votes were most likely to be for Bush when they
were opened, and fight in advance only for their inclusion. 104 In other
words, the votes Bush tried to add had a very high D--and so a high
expected value-and a very low variance, which is precisely the sort of
votes to which a recount defender should limit his requests.
Democratic efforts to be strict about the rules and exclude these votes,
however legally legitimate, were unpopular and soon disclaimed not only
by Florida's Democratic Attorney General Robert Butterworth, but by
vice-presidential candidate Joseph Lieberman as well. It didn't help that
Gore's public stance elsewhere was to count every vote. But Gore's team
had a second-best option: if they couldn't get these legally questionable
votes all tossed out, they could at least have raised D by getting them all
counted instead of allowing the Bush team to cherry-pick a favorable
subset of them. Instead, Gore's team essentially conceded this part of the
game, and with it over 100 net votes. 105
3. The Contest Phase
By the time that the protest phase was over, it was clear that Gore's
strategy of seeking only limited recounts was flawed. Among the Big 3,
only Broward had completed its recount on time. Even if they had
completed their recounts in time, moreover, Palm Beach and Miami-Dade
did not look like they held enough sure votes to swing the election to Gore.
The contest phase gave Gore a new chance to redeem himself and seek a
broader recount, with higher n, V, and variance, and he considered various
additional components to add to his strategy. 106 Instead of taking the
102
See Bickerstaff, supra note 6, at 189-90 (describing Bush strategy).
See id. at 190.
Barstow & Van Natta, supra note 29, at 17 (describing Bush strategy and conduct regarding
overseas absentee ballots).
105
See id. at 17-18 (providing a comprehensive account of the handling of overs·eas ballots).
Barstow and VanNatta reported the Bush gain as 109 net votes; other sources put it at 123 votes. See,
e.g., TOOBIN, supra note 5, at 176. The latter number better reflects the county-by-county vote totals
found in the Appendix, but that includes other changes as well.
106
Bickerstaff, supra note 6, at 196 (describing options Gore considered for the contest).
103
104
174
Journal of Law & Politics
[Vol.XXX:l41
opportunity to jettison his flawed strategy, however, Gore decided to
double down on it.
Recall that in his contest action, Gore sought five things. The firstusing an incomplete count from Nassau rather than an earlier, more
complete one-was doomed to failure and his team knew it. 107
The next was to count the slightly tardy results of the Palm Beach
recount, worth 215 net votes (but not really), and the partial recount from
Miami-Dade, worth another 168. 108 This was not enough to overcome his
537-vote deficit, though.
The question for Gore, therefore, was where else to look for votes. The
obvious place, based on optimal recount strategy, would have been to
maximize n, V, and variance by looking anywhere and everywhere there
might be net Gore votes. There was a good legal argument to be made that
counting every vote was the right thing to do, especially with hundreds of
rejected ballots to inspect per vote separating the candidates. Although it
requires hindsight to know that the Florida Supreme Court ordered a
statewide recount-that, in other words, Gore would have found a
receptive audience if he had argued in court for a broader count-the fact
that Gore's lawyers resisted when the Court started hinting in that direction
during oral arguments shows that Gore's team was fiercely committed to
its low n, low V, low variance, low P strategy. 109
a) The Big 3 Were Not Enough
So, instead of looking statewide for new votes, Gore chose two places,
both of which he had already attempted before: the rest of Miami-Dadejust the undervotes this time-and the dimpled chad of Palm Beach. His
strategy for the contest phase was thus essentially to re-fight the protest
phase; he sought to wring all the votes he needed out of the Big 3, and to
107
Gore sought to use Nassau's second count, which had left out about 200 votes in a way
favorable to Gore. Nassau officials knew exactly where the votes in question were; they testified in the
contest that the votes had been found and were sealed up in a box. Gore could have asked for the box to
be opened and the votes to be counted, but he did not. If he had, he knew he would have lost. But his
argument to revert to the first, smaller count had no legal foundation. Gore's Vnet for his Nassau County
argument was 51 with a variance of zero, but his L was virtually zero, with a variance of virtually zero
as well. Thus, Gore's best estimation for the value of the Nassau argument should have been zero, with
zero variance. It appears that this was, indeed, how his lawyers saw it. See TAPPER, supra note 4, at
387.
108
See supra text accompanying notes 72-76.
109
See TAPPER, supra note 4, at 412, 414 (recounting David Boies's argument to Florida Supreme
Court on behalf of Gore).
2014]
Winning Recounts
175
continue to avoid recounts in the Bush-friendly remainder of the state. Not
only did this approach ignore the benefits of a wider search for votes, it
was never likely to yield enough votes to win anyway. To be sure, with a
positive expected value these arguments were worth including. Perhaps
they might have even been at the top of the list of recount options worth
including. They were not, however, the only things worth including. They
were clearly not enough to justify any notion that Gore's P was greater
than 50%.
First, the dimples. It was known that of Broward's 567 net votes for
Gore, 420 of them came from dimpled chads. 110 Similar proportions were
evident, if not precisely known, in Palm Beach. Gore understood this, and
it is why he fought to have the court count the Palm Beach dimples.
However, the problem was another variable: L. Gore was asking for more
of Palm Beach's presidential dimples to be counted as votes; Palm Beach
had counted dimples only when the voter made dimples all through the
ballot. 111 Gore was following the optimal strategy here, at least-he sought
to maximize V, and variance with it. But Palm Beach's standard made
sense, and it was not going to be easy for Gore to convince the courts that
an isolated dimple had to count as an expression of voter intent. Gore's
argument was also complicated by the fact that his partisans on the ground
had not pressed for a more inclusive standard during the Palm Beach hand
recount itself. 112 Even if it was an argument worth making-and it was,
since if successful, it would have delivered Gore enough votes to win the
election 113-this was not an argument worth banking on.
Second, the remainder of Miami-Dade. Using the crudest of
calculations, Gore argued that because he had gained 168 from an
examination of a fifth of Miami-Dade's undervote, he could expect to gain
600 more from an examination of the rest of them. This expectation was
ludicrous, and it was obvious at the time that it was ludicrous. The partial
recount had covered some of Gore's strongholds; overall he won these
precincts three to one in the initial count. The remainder of the county had
supported Bush by a slight margin, and so promised to be unhelpful for
110
See Jan Crawford Greenburg, Mistake in Citing Illinois Case Gives Bush Ammo, CHI. TRIB.,
Dec. I, 2000, at I.
111
See supra text accompanying note 76.
112
Bickerstaff, supra note 6, at 187 (describing how Gore team pushed for inclusive counts in other
counties, but not Palm Beach). Moreover, Gore had the burden of introducing evidence (as opposed to
mere argument) that Palm Beach had rejected legal votes, but he introduced none. See id at 200.
113
See id at 186 & nn.154-55.
176
Journal ofLaw & Politics
[Vol.XXX: 141
Gore if recounted. All of this information was available at the time, and it
seems as though at least some people in the Gore camp understood it. 114
If one "ecologically regressed" Miami-Dade's undervote-i.e., divided
it up precinct-by-precinct according to the candidates' respective
proportions of votes in the initial count-Gore had a potential net gain of
1,676 votes in the entire county. The partial recount revealed, however,
that only about 20% of the ballots revealed a choice; discounting for this
drops Gore's expected gain to about 344 votes. Of these 344 votes, though,
229 come from precincts included in the partial recount, leaving Gore with
only 115 net votes from the remainder of the county, rather than the 600 he
surmised. 115 But even 115 was too much, given the disproportionately poor
showing Gore made in all of the punch-card hand counts. After all, the
partial recount had not netted Gore 229 votes, but only 168, because Gore
voters in Miami-Dade were actually more likely to punch out their chad
properly than Bush voters were. Taking this into account, Gore reasonably
should have expected either to gain very little from the remainder of
Miami-Dade, or actually to lose ground. 116 He had no reasonable basis to
expect to gain even 100 net votes, let alone the 600 he claimed.
b) The Rest of the State, Scan Ballots, and Overvotes
Thus, the P from Gore's contest was small, and certainly below 50%.
This probability takes us back once more to the counterintuitive core of the
optimal recount strategy for a challenger. The only time a challenger
should not seek to include a group of votes in a recount is if they not only
are expected to favor the opponent, but are expected to do so with a high
114
See TAPPER, supra note 4, at 280 (noting distribution of Miami-Dade undervotes); id. at 379
(attributing belief to Gore lawyer David Boies that "he's not even sure Gore would gain votes" in the
remainder of Miami-Dade); Bickerstaff, supra note 6, at 200-{)1. I myself made this point at the time.
See John Fund, The Myth of Miami, OPINIONJOURNAL.COM (Nov. 26, 2000, II :59 PM),
http://online.wsj.com/news/articles/SBI22416778513540613 (quoting the high end of my estimate of
likely results and noting that "Mr. Kalt's analysis squares with that of other political observers").
115
Precinct-by-precinct results in the initial count and partial recount, from which these
calculations are derived, are available at Bruce Hansen's Florida Data Page,
http://www.ssc.wisc.edu/-bhansen/vote/dadedata.xls (last visited Mar. 3, 2014). The data match the
numbers
from
the
official
county
website,
http://www.miamidade.gov/elections/results/ele00312/CANVOOOl.HTM (last visited Mar. 3, 2014).
Neither data set matches the official totals, however; the totals are irreconcilable. They are close
enough for present purposes, though.
116
The Miami Herald's recount put his loss from the remainder of the undervotes at 135. Amy
Driscoll, Review of Undervotes Includes Dimples, Chads, Clean Punches, MIAMI HERALD, Feb. 26,
200l,at 17A.
2014]
Winning Recounts
177
degree of certainty (i.e., low variance). To see what Gore should have tried
to do with the ballots outside the Big 3, therefore, we must survey what he
knew or should have known about them.
Although it may never be known exactly what Gore and his team
actually knew, some data were clearly available during the;; election
controversy itself. Whether or not Gore's team knew these things, it is a
very matter of basic recount strategy to try to collect such data. 117 At the
very least, any facts that were reported in newspapers at the time were
constructively known to the campaigns themselves.
By the time the protest phase was over on November 26, a lot of things
were definitely known. Every county had done at least some recounting,
and Volusia, Broward, and Palm Beach had done complete hand recounts.
Gore also had a large team of partisans who could have spent the
intervening time collecting data. 118 The Miami Herald ran a story on
December 3 in which it allocated all of the undervotes and overvotes
statewide according to precinct-level voting percentages. 119 Certainly
Gore's team could have acquired precinct-level data even faster, to get a
better idea of where recounts would help or hurt the most.
One source of broader information was Volusia, which performed the
first and fastest protest-phase recount. Because Volusia used scan ballots
rather than punch cards, the process was not bogged down in the
interpretation of chad, and it was less than half the size of Palm Beach, the
smallest of the Big 3. Its hand recount was completed on November 14,
before hand counting in the Big 3 had even begun. 120
Because Gore had won Volusia by an 8% margin, he could have been
comfortable in the knowledge that he was likely to gain some net votes
from a Volusia recount. He did, netting 98 votes. Among the hundreds of
votes that were machine-rejected but added after hand inspection, Gore
picked up almost twice as many as Bush 121 -further evidence of Gore's
117
Good, precinct-level data on county tallies were quickly available on some county websites, and
at Bruce Hansen, Florida Data Page, http://www.ssc.wisc.edu/-bhansen/vote/ data.html (last visited
Mar. 3, 2014). From my perch in Michigan, I personally collected other data and explanations by
contacting individual county elections officials; Gore's team did the same. TOOB!N, supra note 5, at 84
(describing Gore team's activities).
118
Cf Bickerstaff, supra note 6, at 208 (criticizing Gore team's subpar organization and
information gathering).
119
Anabelle de Gale et al., A Flawless Vote Would Have Shown a Winner: Analysis Finds an Edge
for Gore, MIAMI HERALD, Dec. 3, 2000, at I A.
120
See Bickerstaff, supra note 6, at 184-85.
121
TAPPER, supra note 4, at 181 (reporting 241-143 Gore margin in Vol usia recount).
178
Journal of Law & Politics
[Vol.XXX:141
disproportionate yield among hand-counted scan ballots; of how quickly
scan ballots could be hand counted; and of the rich potential of overvotes.
In sum, it was further evidence that Gore lacked the combination of
negative expected value and low variance that would have justified
excluding the rest of the state from his requested recounts.
It is one of the enduring mysteries of the recount why Gore
concentrated in the contest on undervotes to the exclusion of overvotes. 122
Perhaps it was simply that hand inspection of an undervote could reveal a
choice that the machine had missed, while overvotes seemed
unsalvageable; if a person voted for more than one candidate, how could
you tell which one the voter supported?
This reasoning made more sense for the punch-card ballots that Gore
focused on so single-mindedly. A punch-card reader might miss a vote if
the requisite piece of chad failed to detach completely (an undervote). If
the piece of chad, though still attached, was affected enough for a human
to notice, the intent of the voter might be determined. It is hard to see,
however, how the machine might mistakenly count a piece of chad as
punched out when it was still in place (an overvote). Once more than one
piece of chad is punched out, moreover, there generally would be no way
to determine which one of the two an individual voter meant to choose.
On scan ballots, however, overvotes were not necessarily
undecipherable. In some cases, erasures, spillover, and stray marks might
have been misinterpreted as votes by the machine but easily interpreted
correctly by human eyes. Moreover, as already discussed, redundant writein votes were unfortunately common. 123
These possibilities for recovering scan overvotes would have been well
known to anyone who had conducted a recount before-as people on
Gore's team had. 124 Even if they were not so obvious, they were revealed
very early in the recount. It was reported in the Orlando Sentinel on
November 14 that several counties, aware that voters had cast redundant
122
See Bickerstaff, supra note 6, at 194-95 (discussing Gore team's puzzling but fatal disregard for
the potential gains from overvotes).
123
See supra text accompanying notes 54-55. The same error was possible in punch-card counties
too, if voters were directed to punch a hole to indicate that they were writing in a choice, but that was
not generally the case. See, e.g., MARTIN MERZER ET AL., THE MIAMI HERALD REPORT: DEMOCRACY
HELD HOSTAGE 154{(2001) (showing Palm Beach punch-card ballot).
124
See DOWNS ET AL., supra note I, at 31-34 (describing recoverability of scan overvotes);
TAPPER, supra note 4, at 184, 193-94.
2014]
Winning Recounts
179
write-in votes, had decided not to count them. 125 But other counties, like
Gadsden and Orange, had counted these votes by hand, and revealed that
Gore voters had cast a greatly disproportionate number of them; this
evidence was known during the automatic recount, in the first days of the
whole recount episode. 126 Despite this evidence that Gore could pick up a
lot of votes quickly from hand counts in scan counties, he never asked to
count them, instead relying on the Big 3 and on undervotes in his
arguments before the Florida and U.S. Supreme Courts.
This determination may have been based on the fact that scan counties
tended to be Republican, and that Orange and Gadsden, two Democratic
counties, had apparently already been recounted. But Orange and Gadsden
had shown that Gore voters were much more likely to cast redundant writein ballots than were Bush voters. Moreover, even without this direct
evidence of a favorable D, it was still worth taking the chance. Even
though the scan ballots were mostly found in counties that, on balance,
favored Bush, there was no basis to conclude with such certainty that
recounting them would have favored Bush. Gore should have sought to
recount them. 127
Another reason that Gore might have disregarded the scan counties was
that they tended to be small. Although they represented 41 of Florida's 67
counties, they represented only 38% of the total votes cast, and only 18%
of the rejected ballots. 128 (There were other punch-card counties outside the
Big 3, but they too tended to be smaller.)
Obviously, though, 18% was not zero. Maximizing n, V, and variance
means not writing off large heaps of potential votes. Higher n and V are
valuable, even if they come from collecting a lot of crumbs. In this case,
the crumbs added up to a rather large slice. While each additional county
would have represented an expense of resources to the Gore campaign,
small counties could execute hand recounts more quickly than large ones
125
Maxwell & Damron, supra note 54.
See supra text accompanying notes 53-55.
In a misstep, Bush's team argued that if undervotes were reexamined, overvotes would need to
be reexamined too. This argument was obviously contrary to the optimal strategy for defenders, and
would have been costly-possibly fatal-to Bush's chances had it succeeded. See David Damron &
Roger Roy, Both Teams Misjudged Strategy to Win Recount, ORLANDO SENTINEL, Nov. 12, 2001, at
B I, available at 200 I WLNR I 0878414.
128
Information on the number of rejected ballots, grouped by voting method, appears in the
Appendix.
126
127
180
Journal of Law & Politics
[Vol.XXX: 141
like the Big 3. 129 As Vol usia's recount suggested, scan-ballot recounts also
would have been less controversial as they would not have turned on the
interpretation of the myriad types of mis-punched chad. 130
Importantly, many scan counties rejected ballots at a much higher rate
than the punch-card counties. There were two types of scan counting
systems. In one, "precinct scan," each precinct had scanning equipment so
that if a ballot was rejected, the voter found out immediately and could
correct it. In the other system, "central scan," all of the ballots were sent to
a central county office and scanned there, giving the voter no opportunity
to fix an error. Not surprisingly, the rate of rejected ballots was much
higher in central-scan counties (5.63%) than in precinct-scan counties
(0.80%), but it was also higher than in the much-ballyhooed punch-card
counties (3.92%). 131 In Orange County, a precinct-scan county, almost onefourth of the rejected ballots came from a single precinct where a poll
worker did not give voters a chance to fix their rejected ballots; this poll
worker's actions alone cost Gore a net of 60 votes. 132 If Gore's team had
wanted to limit the scope of the scan-ballot recounts, it could have at least
focused on the central-scan counties, instead of pretending that punch
cards were the only problem in Florida.
Put in terms of optimal recount strategy, recounts in these counties
might have appeared at first to have a low D for Gore, along with low n
and low V. But there was evidence that D was actually quite good, and
even without that, adding any n and Vis good when it comes with enough
variance. The same goes for the punch-card counties outside the Big 3, and
the counties using other voting systems.
To summarize, the only way that Gore should have brought a contest as
limited as the one he did was if the elements he chose gave him a P of
greater than 50%. At that point, he would have been justified in behaving
like a defender, seeking to avoid recounting any other groups of votes
unless he was reasonably sure they would help him. But Gore should not
have felt that way about the P presented by his limited contest. He should
129
See Gary Kane and Scott Hiaasen, Optical Scanners Deliver Quicker Ballot Recounts, PALM
BEACH POST, Nov. 16, 2000, at 14A, available at 2000 WLNR 1688197.
130
See supra text accompanying note 120 (discussing Volusia).
131
lnfonnation on the number of rejected ballots, grouped by voting method, appears in the
Appendix.
132
Roger Roy & Michael Griffin, Errors Cost Orange Votes: Some Poll Workers Ignored
Warnings, ORLANDO SENTINEL, Feb. 4, 2001, at AI, available at 2001 WLNR 10891094 (describing
Orange debacle).
2014]
Winning Recounts
181
have sought more votes, and more variance. A statewide recount would
have provided plenty of both.
4. Other Foibles
As mentioned already, there is now no doubt that the butterfly ballot in
Palm Beach led to thousands of Gore voters miscasting their ballots, either
overvoting for both Gore and Pat Buchanan, or erroneously marking just
Buchanan. 133 Thousands more in Duval, where the presidential candidates
were listed on two pages, voted for Gore and voted again for another
candidate on the second page. 134 It is beyond any reasonable doubt that, in
statistical terms, a huge number of Gore votes were lost in these
manners. 135 If they had been converted into "legal" votes, Gore would have
won by a comfortable margin. These lost votes may be the reason why
Gore led in exit polls, and why his team might have been more apt than it
should have been to approach the recount as cautious favorites rather than
hungry underdogs. 136 Nevertheless, Gore's team did realize---<:orrectlythat there was little they could do to obtain these virtual votes. 137 To the
extent that there was some chance of legal success, Gore could and did rely
on third parties to press these cases, but he did not bank on their success. 138
It also emerged in the immediate aftermath of the election that
Republican elected officials in Seminole and Martin Counties had allowed
Republican party activists to correct absentee ballot applications. These
applications, sent out by the Republican party, had incomplete information
because of a printing error. It could not be determined how many of these
applications led to ballots actually being cast for Bush: these voters might
have not voted, voted in person, obtained absentee ballots in some other
manner, or voted for someone other than Bush. Still, the number of fixed
applications was large enough that just about any remedy involving the
exclusion of such votes would have resulted in a large enough net gain for
Gore to reverse the election result. In the case of Seminole and Martin,
moreover, Gore did not want to be in the position of advocating for the
disenfranchisement of any voters, even ones that he knew favored his
133
See Bickerstaff, supra note 6, at 172 (describing Palm Beach problems).
See id. at 173 (describing Duval problems).
135
See Wand et al., supra note 20 (analyzing effect of butterfly ballot).
136
TOOBIN, supra note 5, at 18 (describing exit poll results). But see TAPPER, supra note 4, at 2930 (recounting errors and incompetence in the exit polling).
137
See supra note 12 and accompanying text.
138
See Bickerstaff, supra note 6, at 176 (describing third-party suits).
134
182
Journal ofLaw & Politics
[Vol.:XXX: 141
opponent. This preference was no doubt underscored by the fact that
Gore's team knew that their chances of success in court were slim. 139
It must have been galling for Gore's team to know that these things had
cost their candidate the presidency but that there was little they could do
about them. The Palm Beach and Duval debacles represented a failure of
the most basic task of election administration: accurately collecting and
reporting voters' preferences. But as a matter of recount strategy, Gore's
team got this part of the analysis right, recognizing that L was so low here
that actions in these counties would have added virtually nothing to P.
III. SUMMARY AND CONCLUSION
The optimal recount strategy described in this Article derived the
following lessons:
1. Challengers will seek recounts if they are better off with one than
without one.
2. Challengers will win when they find more new votes than they are
behind by, and successfully convert them into actual votes (if L · Vnet >
M). The probability of this occurring is P.
3. All other things being equal, challengers maximize P by:
a) casting as many votes as possible into question (maximizing nand V).
b) increasing D, the probability that a new vote will go to them instead of
their opponents.
c) increasing the uncertainty (variance) of the predicted results of the
count.
4. Variance will be significantly higher than a simple bell-curve model
would suggest.
5. Variance will increase the less reliable the first count is, the less reliable
the recount is, and the less consistent the recount method is with that of
the first count.
6. In a recount with discrete subgroups of votes to recount, challengers
should try to include those groups where the expected value of Vnet is
139
See TAPPER, supra note 4, at 329.
2014]
Winning Recounts
183
positive, or if not, where the variance associated with the prediction is
sufficiently high. Given Point #4 above, this will more often be the case
than one might think.
7. Defenders, or challengers whose P exceeds 50%, should try to include
subgroups of votes only if their expected value is positive and the
variance is sufficiently low-votes that they expect to help them, so
long as they are sure of that.
Hindsight is irresistible here, given the time, money, and effort that
went into the media's thorough examination of the Florida ballots in the
months following the election. That review showed that the best way for
AI Gore to have won would have been if Florida had recounted all the
undervotes and overvotes statewide. 140
The point is not that challengers always win if they seek the broadest
recounts or the most liberal possible standards. The fact remains that
whatever strategy they use, recount challengers usually lose, even if Gore
might have won here. 141 The point is to maximize one's chances of
success, not to somehow guarantee it. Ex ante, the broader the recount and
the more liberal the standard, the better the odds are for challengers. To put
Point #6 above into layman's terms, recount challengers should seek to
recount not just votes that they expect to help them, but also votes that they
expect to hurt them, so long as they are not too sure of that. AI Gore's
recount lawyers understood this. Gore and his political advisers did not,
and that is why Gore lost the presidency.
140
See Cauchon & Drinkard, supra note 3.
Ironically, the more liberal the standard for counting punch-card votes, the better Bush would
have done. See id. Broader counts mean better odds for challengers, but by no means do they represent
a sure thing.
141
Journal ofLaw & Politics
184
[Vol.XXX:141
APPENDIX
Table 1. Certified vote totals and percentages by county·
County
Alachua
Baker
Bay
Bradford
Brevard
Broward
Calhoun
Charlotte
Citrus
Clay
Collier
Columbia
DeSoto
Dixie
Duval
Escambia
Flagler
Franklin
Gadsden
Gilchrist
Glades
Gulf
Hamilton
Hardee
Hendry
Hernando
Highlands
Hillsborough
Holmes
Indian River
Jackson
Jefferson
Lafayette
Lake
Lee
Leon
Levy
Liberty
Madison
Manatee
Marion
Martin
Miami-Dade
Monroe
Nassau
Okaloosa
Total Votes
85,757
8,155
58,876
8,675
218,488
575,239
5,175
66,900
57,248
57,559
92,202
18,514
7,812
4,667
265,181
116,856
27,116
4,645
14,731
5,395
3 365
6,148
3,966
6 236
8 139
65 236
35 152
360,354
7 396
49 627
16,303
5 643
2 505
88 611
184 400
103 154
12 730
2 410
6 163
110,344
102,971
62 016
625 552
33 895
23 787
70 819
Bush
34,135
5,611
38,682
5,416
115,253
177,939
2,873
35,428
29 801
41,903
60,467
10,968
4,256
2,697
152,460
73 171
12,618
2,454
4,770
3,300
I 841
3 553
2 147
3 765
4 747
30 658
20207
180 794
5 012
28 639
9 139
2 478
I 670
50010
106 151
39 073
6 863
I 317
3 038
58 023
55 146
33 972
289 574
16 063
16408
52 186
Gore
47,380
2,392
18,873
3,075
97,341
387,760
2,156
29,646
25,531
14,668
29,939
7,049
3,321
1,827
108,039
40,990
13,897
2,047
9,736
1,910
I 442
2,398
1,723
2 342
3 240
32 648
14169
169 576
2 177
19 769
6 870
3 041
789
36 571
73 571
61 444
5 398
I 017
3 015
49 226
44 674
26 621
328 867
16487
6 955
16989
Other Bush% Gore%
4,242 39.80% 55.25%
152 68.80% 29.33%
1,321 65.70% 32.06%
184 62.43% 35.45%
5,894 52.75% 44.55%
9,540 30.93% 67.41%
146 55.52% 41.66%
1,826 52.96% 44.31%
1,916 52.06% 44.60%
988 72.80% 25.48%
1,796 65.58% 32.47%
497 59.24% 38.07%
235 54.48% 42.51%
143 57.79% 39.15%
4,682 57.49% 40.74%
2,695 62.62% 35.08%
601 46.53% 51.25%
144 52.83% 44.07%
225 32.38% 66.09%
185 61.17% 35.40%
82 54.71% 42.85%
197 57.79% 39.00%
96 54.14% 43.44%
129 60.38% 37.56%
152 58.32% 39.81%
I 930 47.00% 50.05%
776 57.48% 40.31%
9,984 50.17% 47.06%
207 67.77% 29.43%
1,219 57.71% 39.84%
294 56.06% 42.14%
124 43.91% 53.89%
46 66.67% 31.50%
2 030 56.44% 41.27%
4 678 57.57% 39.90%
2 637 37.88% 59.57%
469 53.91% 42.40%
76 54.65% 42.20%
110 49.29% 48.92%
3 095 52.58% 44.61%
3 151 53.56% 43.39%
I 423 54.78% 42.93%
7 Ill 46.29% 52.57%
I 345 47.39% 48.64%
424 68.98% 29.24%
I 644 73.69% 23.99%
2014]
County
Okeechobee
Orange
Osceola
Palm Beach
Pasco
Pinellas
Polk
Putnam
Santa Rosa
Sarasota
Seminole
St. Johns
St. Lucie
Sumter
Suwannee
Taylor
Union
Vol usia
Wakulla
Walton
Washington
Totals
Winning Recounts
185
Total Votes
Other Bush% Gore%
Bush
Gore
9,854
208 51.32% 46.57%
5,057
4,589
280 155
140 236
5 388 48.02% 50.06%
134 531
55,690
1,266 47.11% 50.61%
26,237
28,187
433,222
10,504 35.31% 62.27%
152,964
269,754
142,769
4,586 48.05% 48.73%
68,607
69,576
13,020 46.38% 50.35%
398,526
200,657
184,849
168,629
90,310
75,207
3,112 53.55% 44.60%
26239
13 457
12 107
675 51.29% 46.14%
50,402
1,245 72.10% 25.43%
36,339
12,818
160,977
4,991 51.63% 45.27%
83,117
72,869
2,788 55.00% 42.98%
137,805
75,790
59,227
60,771
1,698 65.10% 32.10%
39,564
19,509
77,990
1,725 44.50% 53.29%
34,705
41,560
497 54.48% 43.29%
22 261
12 127
9 637
12,461
8,009
4,076
376 64.27% 32.71%
6,810
4,058
2 649
103 59.59% 38.90%
3,826
2,332
1,407
87 60.95% 36.77%
183,674
82,368
97,313
3,993 44.84% 52.98%
8,587
4,512
3,838
237 52.54% 44.70%
18 323
12 186
5 643
494 66.51% 30.80%
8,026
4,995
2,798
233 62.24% 34.86%
5 963110 2 912 790 2 912 253 138 067 48.85% 48.84%
• Source: Dave Leip's Atlas of U.S. Presidential Elections- Data Graphs, http://uselectionatlas.org/
RESULTS/datagraph.php?year=2000&fips=12&f=l &off=O&elect=O (last visited March 3, 2014).
Journal of Law & Politics
186
[Vol.:XXX: 141
Table 2. Results by county: initial count (1118); automatic recount (I 1114);
late overseas absentees (11118); final recounts and certified totals (I 1126/
County
Alachua
Baker
Bay
Bradford
Brevard
Broward
Calhoun
Charlotte
Citrus
Clay
Collier
Columbia
DeSoto
Dixie
Duval
Escambia
Flagler
Franklin
Gadsden
Gilchrist
Glades
Gulf
Hamilton
Hardee
Hendry
Hernando
Highlands
Hillsborough
Holmes
Indian River
Jackson
Jefferson
Lafayette
Lake
Lee
Leon
Levy
Liberty
Madison
Manatee
Marion
Martin
Miami-Dade
Monroe
Initial Count
Bush
34,062
5,610
38,637
5,413
115,185
177,279
2,873
35,419
29,744
41,745
60,426
10,964
4,256
2,698
152,082
73,029
12,608
2,448
4,750
3,300
1,840
3,546
2,153
3,764
4,743
30,646
20,196
180,713
4,985
28,627
9,138
2,481
1,669
49,963
106,123
39,053
6,860
1,316
3,038
57,948
55,135
33,864
289,456
16,059
Gore
47,300
2,392
18,850
3,072
97,318
386,518
2,155
29,641
25,501
14,630
29,905
7,047
3,322
1,825
107,680
40,958
13,891
2,042
9,565
1,910
1,440
2,389
1,718
2,341
3,239
32,644
14,152
169,529
2,154
19,769
6,868
3,038
788
36,555
73,530
61,425
5,403
1,011
3,011
49,169
44,648
26,619
328,702
16,483
Final
Automatic Late Overseas
Absenteest
Recounts~
Recount **
Bush Gore Bush Gore Bush Gore
15
62
65
II
1
0
0
0
18
7
5
0
0
38
1
3
2
0
14
6
54
17
0
0
44
43
37
53
579 1,146
1
0
0
0
I
7
4
2
22
24
34
6
1
0
-9
2
154
13
1
35
13
11
25
10
7
9
0
0
4
2
-2
0
0
I
-1
1
I
0
16
184
151
44
24
318
-12
-15
45
109
38
9
5
6
5
0
4
6
0
I
170
17
3
I
0
0
0
0
I
2
0
0
4
8
I
3
-7
4
I
1
-2
I
0
3
4
1
0
0
0
0
12
4
10
15
I
2
47
28
34
19
26
23
I
0
-1
8
4
I
0
0
I
2
-3
3
0
0
I
1
0
0
47
16
36*
18*
18
30
10
II
9
2
11
17
-2
-5
5
0
I
6
0
0
0
3
0
I
4
12
8
55
37
16
17
6
5
9
106
1
I
2
100
77
41
59
0
6
0
0
4
4
Certified Totals
Bush
34,135
5,611
38,682
5,416
115,253
177,939
2,873
35,428
29,801
41,903
60,467
10,968
4,256
2,697
152,460
73,171
12,618
2,454
4,770
3,300
1,841
3,553
2,147
3,765
4,747
30,658
20,207
180,794
5,012
28,639
9,139
2,478
1,670
50,010
106,151
39,073
6,863
1,317
3,038
58,023
55,146
33,972
289,574
16,063
Gore
47,380
2,392
18,873
3,075
97,341
387,760
2,156
29,646
25,531
14,668
29,939
7,049
3,321
1,827
108,039
40,990
13,897
2,047
9,736
1,910
1,442
2,398
1,723
2,342
3,240
32,648
14,169
169,576
2,177
19,769
6,870
3,041
789
36,571
73,571
61,444
5,398
1,017
3,015
49,226
44,674
26,621
328,867
16,487
2014]
County
Nassau
Okaloosa
Okeechobee
Orange
Osceola
Palm Beach
Pasco
Pinellas
Polk
Putnam
Santa Rosa
Sarasota
Seminole
St. Johns
St. Lucie
Sumter
Suwannee
Taylor
Union
Volusia
Wakulla
Walton
Washington
Totals
Bush Lead
Winning Recounts
Initial Count
Bush
Gore
16,404
6,952
16,924
52,043
5,058
4,588
134,476
140,115
26,216
28,177
152,846
268,945
68,581
69,550
184,884
200,212
90,101
74,977
13,439
12,091
36,248
12,795
83,100
72,854
75,293
58,888
39,497
19,482
34,705
41,559
12,126
9,634
8,014
4,084
4,050
2,647
2,326
1,399
82,214
97,063
4,511
3,835
12,176
5,637
4,983
2,796
2,909,135 2,907,351
1,784
187
..
Automatic Late Overseas
Final
Certified Totals
Absenteest
Recounts:
Recount
Bush
Gore
Bush Gore Bush Gore Bush Gore
16,408
-124
-73
3
3
125
73
6,955
52,186
I
16,989
50
24
91
40
2
-I
5,057
4,589
0
0
I
134,531 140,236
41
105
14
16
-4
26,237
28,187
4
25
6
152,964 269,754
105
787
13
22
68,607
69,576
I
14
13
6
12
6
184,849 200,657
I
-61
417
24
27
2
194
4
90,310
75,207
223
4
3
II
13,457
II
12,107
8
10
5
26
36,339
12,818
7
36
8
29
8
-I
83,117
72,869
0
17
16
384
113
75,790
59,227
53
286
19,509
39,564
49
20
18
7
41,560
0
0
0
I
34,705
12,127
1
3
9,637
0
0
4,076
-8
8,009
-9
3
I
2,649
6
2
2
0
4,058
6
2,332
1,407
0
0
8
143
241
II
82,368
9
97,313
I
4,512
3
0
0
3,838
4
12,186
6
5
1
5,643
It
2
I
4,995
2,798
0
1,357 2,841 1,380
750
918 1,311 2,912,790 2,912,253
-1,484
+630
-393
537
• Sources: Latest County-by-County Results, MIAMI HERALD, Nov. 15, 2000, at 19A (automaticrecount results, from which initial results can be derived); David Firestone, Hand Tallies Go On, N.Y.
TIMES, Nov. 19, 2000, at 1 (overseas absentee results); Florida Recount, WASHINGTONPOST.COM,
http://www. washingtonpost.com/wp-srv/onpoli tics/elections/flacountyrecounts ll2700.htm (last visited
March 3, 2014) (final changes); Dave Leip 's Atlas of U.S. Presidential Elections - Data Graphs,
http://uselectionatlas.org/RES ULTS/datagraph. php?year=2000&fips= 12&f-= I&off-=O&elect=O
(last
visited March 3, 2014) (final totals).
"Includes Volusia County hand recount. Lake County had +II Bush, -2 Gore from the automatic
recount, but also counted military ballots received to that point (+36 Bush, +18 Gore) instead of
waiting until November 17. See Anthony Colarossi, Lake's Absentees Could Be the Key, ORLANDO
SENTINEL, Nov. 16,2000, at I, available at 2000 WLNR 8608612. The military ballots are included in
the total for the automatic recount. They are also listed in the columns for late overseas absentee ballots
but are not included in the totals there.
t Over 12,000 overseas absentee ballots were received by Election Day and are included in the
preliminary count rather than here. See Bryan Gilmer et at., 300 and Counting, ST. PETERSBURG TIMES,
Nov. 15, 2000, at I A, available at 2000 WLNR 8817467.
1 Changes made between November 18 and 26 include the hand recount from Broward; Nassau's
rejection of its automatic recount results; the re-evaluation of overseas absentee ballots (including one
for Bush from Nassau); the sample recount in Miami-Dade; and others not explained. See Florida
WASHINGTONPOST.COM,
http://www.washingtonpost.com/wp-srv/onpolitics/elections/
Recount,
flacountyrecounts112700.htm (last visited March 3, 2014) (listing changes and explaining some); Scott
Hiaasen & Stephen Kiehl, Counties Changed How Overseas Ballots Tallied, PALM PEACH POST, Dec.
2, 2000, at 23A, available at 2000 WLNR 1678266 (listing some results from re-evaluation of overseas
absentee ballots); supra text accompanying note 69 (discussing Nassau).
Journal of Law & Politics
188
[Vol.XXX:141
Table 3. County voting methods and number of rejected ballots
(not reflecting hand recounts/
Voting
Method
Alachua
P Scan
Baker
P Scan
Bay
P Scan
Bradford
C Scan
Brevard
P Scan
Broward
Punch
Calhoun
P Scan
Charlotte
CScan
Citrus
P Scan
Clay
P Scan
Collier
Punch
Columbia
P Scan
DeSoto
Punch
Dixie
Punch
Punch
Duval
Escambia
P Scan
Flagler
P Scan
Franklin
CScan
Gadsden
C Scan
Gilchrist
Punch
Punch
Glades
Gulf
CScan
Hamilton
CScan
Punch
Hardee
Hendry
C Scan
P Scan
Hernando
Highlands
Punch
Hillsborough Punch
P Scan
Holmes
Indian River Punch
Jackson
CScan
Jefferson
Punch
CScan
Lafayette
CScan
Lake
Punch
Lee
P Scan
Leon
Levy_
CScan
Liberty
CScan
Punch
Madison
Manatee
P Scan
Punch
Marion
Machine
Martin
Miami-Dade Punch
Monroe
P Scan
Punch
Nassau
County
Total Over- UnderOver- Under- UnTotal
Total
votes known Rejects vote% vote 0/o Reject%
votes
Ballots
102
225
327 0.12% 0.26%
0.38%
86,056
140 0.55% 1.13%
46
94
1.69%
8,294
134
529
663 0.23% 0.89%
1.11%
59,468
695
40
735 7.39% 0.43%
7.81%
9,407
413 0.06% 0.13%
277
0.19%
136
219,427
7,925 6,686
14,611
1.35% 1.14%
2.48%
588,007
78
87 0.17% 1.49%
1.66%
5,252
9
2,988
4.51%
3,156 4.27% 0.24%
168
70,052
217 0.09% 0.28%
0.38%
54
163
57,418
161
233
394 0.28% 0.41%
0.69%
57,506
1,102 2,086
3,188 1.16% 2.19%
3.34%
95,325
3.61%
19,201
617
76
693 3.21% 0.40%
8.24%
8,506
701
701 0.00% 0.00%
6.64%
332
332 0.00% 0.00%
4,998
26,909 7.53% 1.70%
9.23%
291,545 21,942 4,967
3.61%
4,372 0.00% 0.00%
121,020
4,372
0.23%
27,173
7
55
62 0.03% 0.20%
8.28%
5,063
349
70
419 6.89% 1.38%
12.34%
1,951
122
2,073 11.61% 0.73%
16,800
5.07%
5,683
288
288 0.00% 0.00%
9.58%
3,738
358
358 0.00% 0.00%
411 5.54% 0.73%
6.27%
6,555
363
48
4,353
389
8.94%
0
389 0.00% 8.94%
6,641
323
408 4.86% 1.28%
6.14%
85
761
8.95%
8,938
39
800 0.44% 8.51%
65,467
147
101
248 0.22% 0.15%
0.38%
36,158
520
489
1,009 1.44% 1.35%
2.79%
3,641 5,531
369,467
9,172 0.99% 1.50%
2.48%
7,534
148
148 0.00% 0.00%
1.96%
51,559
879 1,058
1,937 1.70% 2.05%
3.76%
1,063
17,457
94
1,157 6.09% 0.54%
6.63%
6,215
571 0.00% 0.00%
9.19%
571
2,676
6.39%
171
171 0.00% 0.00%
3,114
245
3,359 3.38% 0.27%
3.64%
92,225
2,550 2,017
2.42%
188,944
4,567 1.35% 1.07%
0.18%
181
103,305
181 0.00% 0.18%
5.64%
13,484
708
52
760 5.25% 0.39%
2,598
159
29
188 6.12% 1.12%
7.24%
6,642
481
481 0.00% 0.00%
7.24%
1,263
111,631
1,263 1.13% 0.00%
1.13%
0
900 2,445
3,345 0.85% 2.30%
106,301
3.15%
62,623
175
175 0.00% 0.00%
0.28%
28,601 2.73% 1.64%
654,042 17,851 10,750
4.37%
97
34,058
83
180 0.28% 0.24%
0.53%
1,410
195
25,162
1,605 5.60% 0.77%
6.38%
2014]
County
Okaloosa
Okeechobee
Orange
Osceola
Palm Beach
Pasco
Pinellas
Polk
Putnam
Santa Rosa
Sarasota
Seminole
St. Johns
St. Lucie
Sumter
Suwannee
Taylor
Union
Vol usia
Wakulla
Walton
Washington
Totals
Winning Recounts
Voting
Method
P Scan
CScan
P Scan
Punch
Punch
Punch
Punch
P Scan
P Scan
P Scan
Punch
P Scan
P Scan
P Scan
Punch
CScan
C Scan
Paper
P Scan
Punch
P Scan
P Scan
Total
OverBallots
votes
71,445
680
10,711
774
282,529
1,383
57,341
1,042
462,880 19,120
146,648
2,141
406,956 4,261
671
169,507
26,390
78
50,684
164,180
991
137,904
48
61,304
132
78,638
112
169
23,023
13,173
690
7,407
517
4,084
184,243
155
8,587
18,537
72
8,350
37
6,138,495 106,318
189
Total Over- Under- Total
Under- Unvotes known Rejects vote 0/o vote% Reject%
765 0.95% 0.12%
1.07%
85
858 7.23% 0.78%
84
8.01%
0.83%
2,349 0.49% 0.34%
966
1,684 1.82% 1.12%
2.94%
642
6.42%
29,702 4.13% 2.29%
10,582
3,917 1.46% 1.21%
2.67%
1,776
8,487 1.05% 1.04%
2.09%
4,226
0.53%
228
899 0.40% 0.13%
0.64%
168 0.30% 0.34%
90
325
325 0.00% 0.00%
0.64%
1.71%
1,809
2,800 0.60% 1.10%
0.19%
219
267 0.03% 0.16%
0.91%
426
558 0.22% 0.69%
0.83%
649 0.14% 0.68%
537
3.31%
762 0.73% 2.58%
593
5.56%
732 5.24% 0.32%
42
599 6.98% 1.11%
8.09%
82
6.32%
258
258 0.00% 0.00%
0.33%
603 0.08% 0.24%
448
430
430 0.00% 0.00%
5.01%
1.11%
133
205 0.39% 0.72%
3.94%
292
329 0.44% 3.50%
2.91%
63,682 8,610 178,610 1.73% 1.04%
Summary by voting method
Voting
Total
Over- Under- UnTotal
Over- UnderTotal
#
Method Counties Ballots
votes votes known Re.iects vote% vote% Reject%
P Scan
26 2,072,341 6,141 5,519 4,845 16,505 0.30% 0.27%
0.80%
Machine
62,623
175 0.00% 0.00%
I
175
0.28%
Punch
24 3,718,548 86,767 55,937 3,161 145,865 2.33% 1.50%
3.92%
C Scan
15 280,899 13,410 2,226
171 15,807 4.77% 0.79%
5.63%
Paper
I
4,084
258 0.00% 0.00%
258
6.32%
• Sources: 67 Counties, 4 Voting Methods, PALM BEACH POST, Nov. 26, 2000, at 29A, available at
2000 WLNR 1677446 (voting methods); Susan Schmidt, Statewide Scramble, WASHINGTON POST,
Dec. 9, 2000, at AOI; Jennifer Sergent, 'Under-Votes' and 'Over-Votes' Called Typical in State,
STUART NEWS (Stuart, Fla.), Dec. 3, 2000, at AI, available at 2000 WLNR 7603637 (providing
undervote and overvote totals; some appear to be transposed or missing when compared to Schmidt,
supra, in which case Schmidt's numbers were preferred). Palm Beach's numbers are based on data
obtained from Palm Beach County election officials and my own calculations. See supra note 46. There
are many disparate sources; this does not purport to be a definitive account. See, e.g., 67 Counties 67
Recounts, ST. PETERSBURG TIMES, Nov. 12, 2001, at 6x, available at 2001 WLNR 11081956
(providing total rejection percentages that differ somewhat from those compiled here).
•• P Scan systems tally ballots in the precinct, so that voters have a chance to correct errors. C Scan
ballots are centrally processed and do not afford this opportunity.